FRW Cosmological Models with Bulk-Viscosity in?Barber’s Second Self-Creation Theory

We have studied the evolution of spatially homogeneous and isotropic FRW cosmological model with bulk-viscosity in the frame work of Barber’s (Gen. Relativ. Gravit. 14: 117, 1982) second self-creation theory of gravitation. The cosmological models are obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B: 182, 1983). Physical parameters of the models have been discussed in case of false vacuum model, Zel’dovich fluid and radiation dominated fluid.     

Bianchi Type-III Cosmological Model with Negative Constant Deceleration Parameter in Brans Dicke Theory of Gravitation

Bianchi type-III space time is considered in the presence of perfect fluid source in the scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a cosmological model with negative constant deceleration parameter is obtained in the presence of perfect fluid with disordered radiation. Some physical and kinematical properties of the model are also discussed.     

A Dark Energy Model in a Scale Covariant Theory of Gravitation

An axially symmetric Bianchi type-I space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. Some physical and kinematical properties of the model are also discussed.     

Cosmological Model with Strange Quark Matter Attached to Cosmic String for Axially Symmetric Space-Time

We have investigated cosmological model with strange quark matter attached to the string cloud in general theory of gravitation for Axially Symmetric space time. The model is obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983). Also, some physical and kinematics properties of the model are discussed.     

FRW Cosmological Solution in Self Creation Theory

In this paper, we have investigated spatially homogeneous isotropic Friedman-Robertson-Walker cosmological model with bulk viscosity and zero-mass scalar field in the frame work of Barber’s second self-creation theory (Gen. Relativ. Gravit. 14:117, 1982). The cosmological models are obtained with the help of the special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983) and power law relation. Some physical properties of the models are also discussed.     

Bianchi Type VI String Cosmological Model in Saez–Ballester’s Scalar-Tensor Theory of Gravitation

An exact Bianchi type-VI string cosmological model is obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. 113:467, 1985). Some physical properties of the model are also discussed.     

Axially Symmetric Cosmological Micro Model in Barber’s Modified Theory of Einstein General Relativity

Axially symmetric Bianchi type-I cosmological micro model is obtained in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) modified theory of general relativity. Some properties of the model are discussed.     

An investigation of equivalence between the bulk-based and the brane-based approaches for anisotropic models

We investigate the relation between the brane-based and the bulk-based approaches for anisotropic case in brane-world models. In the brane-based approach, the brane is chosen to be fixed on a coordinate system, whereas in the bulk-based approach it is no longer static as it moves along the extra dimension. It was shown that these two approaches are equivalent for specific models in Mukohyama et al. (Phys Rev D 62:024028, 2000), Bowcock et al. (Class Quant Gravit 17:4745–4764, 2000). In this paper, it is aimed to get general formalism of the equivalence obtained in Mukohyama et al. (Phys Rev D 62:024028, 2000). We found that calculations driven by a general anisotropic bulk-based metric yield a brane-based metric in Gaussian Normal Coordinates by conserving spatial anisotropy. We also derive solutions for an anisotropic bulk-based model and get the corresponding brane-based metric of the model.     

Plane Symmetric Vacuum Bianchi Type-III Cosmological Model in Brans-Dicke Theory

We have obtained an exact solution of the vacuum Brans-Dicke (Phys. Rev. 124:925, 1961) field equations for the metric tensor of a spatially homogeneous and anisotropic model. Some physical properties of the model are also studied.     

Charged anisotropic matter with quadratic equation of state

We extend the work of Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) by considering quadratic equation of state for the matter distribution to study the general situation of a compact relativistic body. Presence of electromagnetic field and anisotropy in the pressure are also assumed. Some new classes of static spherically symmetrical models of relativistic stars are obtained. All the results given in Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) and there in can also be recovered as a particular case of our work.     

Higher Dimensional LRS Bianchi Type-I Domain Walls in a Scalar-Tensor Theory of Gravitation

An exact higher dimensional LRS Bianchi type-I cosmological model is obtained in presence of thick domain walls in a scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A113:467, 1985). Some physical and kinematical properties of the models are also discussed.     

A Macroscopic Model for a System of Swarming Agents Using Curvature Control

In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination of the Vicsek alignment model (Vicsek et al. in Phys. Rev. Lett. 75(6):1226–1229, 1995) and the Persistent Turning Walker (PTW) model of motion by curvature control (Degond and Motsch in J. Stat. Phys. 131(6):989–1021, 2008; Gautrais et al. in J. Math. Biol. 58(3):429–445, 2009). The PTW model was designed to fit measured trajectories of individual fish (Gautrais et al. in J. Math. Biol. 58(3):429–445, 2009). The PTWA model (Persistent Turning Walker with Alignment) describes the displacements of agents which modify their curvature in order to align with their neighbors. The derivation of its macroscopic limit uses the non-classical notion of generalized collisional invariant introduced in (Degond and Motsch in Math. Models Methods Appl. Sci. 18(1):1193–1215, 2008). The macroscopic limit of the PTWA model involves two physical quantities, the density and the mean velocity of individuals. It is a system of hyperbolic type but is non-conservative due to a geometric constraint on the velocity. This system has the same form as the macroscopic limit of the Vicsek model (Degond and Motsch in Math. Models Methods Appl. Sci. 18(1):1193–1215, 2008) (the ‘Vicsek hydrodynamics’) but for the expression of the model coefficients. The numerical computations show that the numerical values of the coefficients are very close. The ‘Vicsek Hydrodynamic model’ appears in this way as a more generic macroscopic model of swarming behavior as originally anticipated.     

A Higher Dimensional Cosmic Domain Wall in Brans-Dicke Theory of Gravitation

Five dimensional Kaluza-Klein Space-time is considered in the presence of thick domain walls in the scalar-tensor theory formulated by Brans and Dicke (Phys. Rev. 124:925, 1961). Exact cosmological model, in this theory, is presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983) for Hubble’s parameter. Some physical and kinematical properties of the model are also discussed.     

A Cosmological Model with Negative Constant Deceleration Parameter in a General Scalar-Tensor Theory of Gravitation

Spatially homogeneous and anisotropic LRS Bianchi type-I metric is considered in the framework of Nordtvedt-Barker’s general scalar-tensor theory of gravitation when the source for the energy momentum tensor is a perfect fluid. With the help of a special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cim. B. 74:182, 1983) a cosmological model with negative constant deceleration parameter is obtained. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter

A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.     

LRS Bianchi Type-I Dark Energy Cosmological Model in Brans-Dicke Theory of Gravitation

Bianchi type-I dark energy model with variable equation of state (EoS) parameter is presented in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To get a determinate solution of the field equations we will take the help of special law of variation for Hubble’s parameter presented by Bermann (Nuovo Cimento B. 74:182, 1983) which yields a dark energy cosmological model with negative constant deceleration parameter. It is observed that this dark energy cosmological model always represents an accelerated and expanding universe and also consistent with the recent observations of type-Ia supernovae. Some physical and geometrical properties of the model are also discussed.     

Description of Heavy Quark [`(MS)]\overline{MS} Mass by Lippmann-Schwinger Equation

Quark masses are of great prominence in high-energy physics. In this paper, we have studied the heavy meson systems via solving the Lippmann-Schwinger equation by using the Martin potential for heavy quark masses. We have also attempted to use Martin potential to find an acceptable mass spectrum for heavy quarkonia. We obtained this spectrum via minimal phenomenological model (Melles in Phys. Rev. D. 62:074019, 2000).     

The Cut Metric,Random Graphs,and Branching Processes

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the sequence of matrices of edge probabilities converges to an appropriate limit object (a kernel), but only in a very weak sense, namely in the cut metric. Our results thus generalize previous results on the phase transition in the already very general inhomogeneous random graph model introduced by the present authors in Random Struct. Algorithms 31:3–122 (2007), as well as related results of Bollobás, Borgs, Chayes and Riordan (Ann. Probab. 38:150–183, 2010), all of which involve considerably stronger assumptions. We also prove corresponding results for random hypergraphs; these generalize our results on the phase transition in inhomogeneous random graphs with clustering (Random Struct. Algorithms, 2010, to appear).     

Calculation of the Isobaric Analogue Resonance Using Shell Model in the Complex Energy Plane

A convenient tool for studying nuclei being far away from the beta stability line is the complex energy shell model (CXSM) in which the Berggren representation (Nucl. Phys. A 109:265, 1968) (BR) is used. The BR is formed from bound, resonant sates, and complex-energy scattering states. The parameters of isobaric analog resonance (IAR) are calculated in the framework of the Lane-model (Nucl. Phys. A 35:676, 1962) using CXSM. The novel feature of the present CXSM calculation is that the optical potentials used are complex. Results of the CXSM calculation are checked against those of the standard solution of the coupled channel Lane-equations (CC). The IAR parameters calculated by the CXSM agree well with that of the CC results for absorptive and emittive optical potentials. This agreement confirms the applicability of the CXSM calculation for complex potential.