We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

The Supernova Legacy Survey: Measurement of Omega_m, Omega_l and w from the First Year Data Set

The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form 
 
$$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$ 
 
, which we solve exactly using a kind of perturbational approach.

Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告)

To find more deliberate f ( R , T ) cosmological solutions, we take our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most acceptable cosmological results. Our investigations are performed by applying the dynamical system approach. We obtain the cosmological parameters/quantities in terms of some defined dimensionless parameters that are used in constructing the dynamical equations of motion. The investigated parameters/quantities are the evolution of the Hubble parameter and its inverse, the “weight function”; the ratio of the matter density to the dark energy density and its time variation; the deceleration; the jerk and the snap parameters; and the equation-of-state parameter of the dark energy. We numerically examine these quantities for two general models R + α R - n + - T and R log [ α R ] q + - T . All considered models have some inconsistent quantities (with respect to the available observational data), except the model with n = - 0.9 , which has more consistent quantities than the other ones. By considering the ratio of the matter density to the dark energy density, we find that the coincidence problem does not refer to a unique cosmological event; rather, this coincidence also occurred in the early Universe. We also present the cosmological solutions for an interesting model R + c 1 - T in the nonflat Friedmann–Lemaitre–Robertson–Walker metric. We show that this model has an attractor solution for the late times, though with w ( DE ) = - 1 / 2 . This model indicates that the spatial curvature density parameter gets negligible values until the present era, in which it acquires the values of the order 10 - 4 or 10 - 3 . As the second part of this work, we consider the weak-field limit of f ( R , T ) gravity models outside a spherical mass immersed in the cosmological fluid. We have found that the corresponding field equations depend on the both background values of the Ricci scalar and the background cosmological fluid density. As a result, we attain the parametrized post-Newtonian parameter for f ( R , T ) gravity and show that this theory can admit the experimentally acceptable values of this parameter. As a sample, we present the post-Newtonian gamma parameter for general minimal power law models, in particular, the model R + c 1 - T .

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Cosmological and Solar System Consequences of f(R,T) Gravity Models

We investigate the cosmological solutions of $f(R,T)$ modified theories of gravity for a perfect fluid in a spatially Friedmann-Lema\^{\i}tre-Robertson-Walker metric through the phase-space analysis, where $R$ is the Ricci scalar and $T$ denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze the three general theories with the Lagrangians of minimal $g(R)+h(T)$, pure nonminimal $g(R)h(T)$, and nonminimal $g(R)(1+h(T))$ couplings through the dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations to more concise forms. The conservation of the energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines the functionality of $h(T)$ to a particular form, and hence relates the dynamical variables. In this case, acceptable cosmological solutions that contain a long enough matter-dominated era followed by a late-time accelerated expansion are found. To support the theoretical results, we also obtain numerical solutions for a few functions of $g(R)$, and the results of the corresponding models confirm the predictions. We separate the solutions into six classes which demonstrate more acceptable solutions and there is more freedom to have the matter-dominated era than in $f(R)$ gravity. In particular, there is a new fixed point which can represent the late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors, and the effective equation of state. The corresponding diagrams of the parameters illustrate that there is a saddle acceleration era which is a middle era before the final stable-acceleration de Sitter era for some models. All presented diagrams determine radiation, matter, and late-time acceleration eras very well. The pure nonminimal theory suffers from the absence of a standard matter era, though we illustrate that the nonminimal theory can have acceptable cosmological solutions.

/pdf/f-r-t-cosmological-models-in-phase-space-2vdraxfzlx.pdf

f ( R , T ) cosmological models in phase space

This paper is devoted to study the possibility of forming anisotropic compact stars in modified Gauss–Bonnet, namely called as f(G) theory of gravity which is one of the strong candidates, responsible for the accelerated expansion of the universe. For this purpose, we have used analytical solution of Krori and Barua metric to the Einstein field equations with anisotropic form of matter and power law model of f(G) gravity. To determine the unknown constants in Krori and Barua metric, we have used the sample of compact stars, 4U1820-30, Her X-1, SAX J 1808-3658. The physical behavior of these stars have been analyzed with the observational data. In this setting, we have checked all the regularity conditions and stability of the compact stars 4U1820-30, Her X-1, SAX J 1808-3658.

Anisotropic compact stars in f(G) gravity

This research explores the solitary wave solutions, including dynamic transitions for a fractional low-pass electrical transmission (LPET) line model. The fractional-order (FO) LPET line mathematical system has yet to be published, and neither has it been addressed via the extended direct algebraic technique. A computer program is utilized to validate all of the incoming solutions. To illustrate the dynamical pattern of a few obtained solutions indicating trigonometric, merged hyperbolic, but also rational soliton solutions, dark soliton solutions, the representatives of the semi-bright soliton solutions, dark singular, singular solitons of Type 1 and 2, and their 2D and 3D trajectories are presented by choosing appropriate values of the solutions’ unrestricted parameters. The effects of fractionality and unrestricted parameters on the dynamical performance of achieved soliton solutions are depicted visually and thoroughly explored. We furthermore discuss the sensitivity assessment. We, however, still examine how our model’s perturbed dynamical framework exhibits quasi periodic-chaotic characteristics. Our investigated solutions are compared with those listed in published literature. This research demonstrates the approach’s profitability and effectiveness in extracting a range of wave solutions to nonlinear evolution problems in mathematics, technology, and science.

/pdf/analytical-analyses-for-a-fractional-low-pass-electrical-1pjvzlp6.pdf

Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

This paper presents a theory of weakly nonlinear wave propagation in superposed fluids in the existence of magnetic fields. The extended direct algebraic approach has been utilized to draw and examine the solitonic wave solutions to the (2+1)-dimensional elliptic nonlinear Schrödinger equation (ENLSE). These obtained solutions are more novel and valuable to researchers for understanding physical marvels. The graphical representation of some selected exact solutions is reported with different parametric values to show their propagation. Furthermore, the examined equation is changed into the planer dynamical structure by utilizing Galilean transformation. By utilizing the idea of bifurcation, all the possible phase portraits of nonlinear and super nonlinear traveling wave solutions have been explored. Moreover, after adding an external force to the dynamical system, the periodic, quasi-periodic, and chaotic behaviors of the 2D, 3D and time series are also observed. Meantime, for various initial conditions, the sensitivity of the derived solutions is investigated in detail. It is discovered that the considered equation is multistable for the same values of parameters but different initial conditions. 

Bifurcation, chaotic and multistability analysis of the $(2+1)$-dimensional elliptic nonlinear Schrödinger equation with external perturbation

Some new wave profiles and conservation laws in a Pre-compressed one-dimensional granular crystal by Lie group analysis

In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1–4 is presented.

Adil Jhangeer

Papers

Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

Bifurcation, chaotic and multistability analysis of the $(2+1)$-dimensional elliptic nonlinear Schrödinger equation with external perturbation

Some new wave profiles and conservation laws in a Pre-compressed one-dimensional granular crystal by Lie group analysis

Classification of static plane symmetric spacetime via Noether gauge symmetries

Conservation Laws For the (1+2)-Dimensional Wave Equation in Biological Environment