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.     

Strange Quark Matter Attached to String Cosmology in FRW Space-Time

We have obtained FRW cosmological model with strange quark matter attached to the string cloud in general relativity. The model is obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983). Also, some physical and kinematics properties of the model are discussed. The results are analogous to results obtained by Yilmaz (Gen. Relativ. Gravit. 38:1397–1406, 2006).     

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.     

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.     

Restoring New Agegraphic Dark Energy in RS II Braneworld

Motivated by recent works (Saridakis in Phys. Lett. B 660:138, 2008; Sheykhi in Int. J. Mod. Phys. D 19(3):305, 2010), we investigate the new agegraphic model of dark energy in the framework of RS II braneworld. We also include the case of variable gravitational constant G in our model. Moreover, we reconstruct the potential and the dynamics of the quintessence, tachyon, K-essence and dilaton scalar field models according to the evolutionary behavior of the new agegraphic dark energy model in RS II braneworld cosmology including varying G.     

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.     

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.     

Quantum-Like Model for Decision Making Process in?Two Players Game A Non-Kolmogorovian Model

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999).     

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.     

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.     

An asymptotic approximation of the Fokker–Planck model of evolution of superthermal ultrarelativistic particles in the presence of interaction scaling

The evolution of a superthermal relict plasma component is studied using a nonequilibrium model of the Universe [1] and a kinetic equation of the Fokker–Planck type [2]. Given is the evidence of two maxima in the distribution of superthermal particles. The first maximum can further evolve into an equilibrium distribution, whereas the second one can result in a high-energy tail of superthermal relict particles. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 87–91, February, 2009.     

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.     

A response to Murshed et al., J Nanopart Res (2010) 12:2007–2010

This brief communication provides a response to Murshed et al. (J Nanopart Res 12:2007–2010, 2010). We acknowledge that three of the equations in our original article (Doroodchi et al. J Nanopart Res 11:1501–1507, 2009) contained minor typographical errors. However, we confirm that these misprinted equations have no bearing on the results presented within that article. In addition, we would like to clarify that we do not challenge the methodology of Leong et al. (J Nanopart Res 8:245–254, 2006). Instead, we repeated their analysis using a more general form for the temperature field with continuity imposed across the particle–nanolayer–liquid interfaces and found that the solution reduces to the Renovated-Maxwell model.     

Charged Polymers in the Attractive Regime: A First-Order Transition from Brownian Scaling to Four-Point Localization

We study a quenched charged-polymer model, introduced by Garel and Orland in 1988 (Europhys. Lett. 6(7):597–601, 1988; Europhys. Lett. 6(4):307–310, 1988), that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the sense that: (1) the rescaled trajectory of the polymer converges to the Brownian path; and (2) the partition function remains bounded.     

Observational Constraints on the Modified Gravity Model (MOG) Proposed by Moffat: Using the Magellanic System

A simple model for the dynamics of the Magellanic Stream (MS), in the framework of modified gravity models is investigated. We assume that the galaxy is made up of baryonic matter out of context of dark matter scenario. The model we used here is named Modified Gravity (MOG) proposed by Moffat (J. Cosmol. Astropart. Phys. 003, 2005). In order to examine the compatibility of the overall properties of the MS under the MOG theory, the observational radial velocity profile of the MS is compared with the numerical results using the χ ² fit method. In order to obtain the best model parameters, a maximum likelihood analysis is performed. We also compare the results of this model with the Cold Dark Matter (CDM) halo model and the other alternative gravity model that proposed by Bekenstein (Phys. Rev. D 70:083509, 2004), so called TeVeS. We show that by selecting the appropriate values for the free parameters, the MOG theory seems to be plausible to explain the dynamics of the MS as well as the CDM and the TeVeS models.     

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.