Scalar Expansion Research Articles

FlexVec: auto-vectorization for irregular loops

Traditional vectorization techniques build a dependence graph with distance and direction information to determine whether a loop is vectorizable. Since vectorization reorders the execution of instructions across iterations, in general instructions involved in a strongly connected component (SCC) are deemed not vectorizable unless the SCC can be eliminated using techniques such as scalar expansion or privatization. Therefore, traditional vectorization techniques are limited in their ability to efficiently handle loops with dynamic cross-iteration dependencies or complex control flow interweaved within the dependence cycles. When potential dependencies do not occur very often, the end-result is under utilization of the SIMD hardware. In this paper, we propose FlexVec architecture that combines new vector instructions with novel code generation techniques to dynamically adjusts vector length for loop statements affected by cross-iteration dependencies that happen at runtime. We have designed and implemented FlexVec's new ISA as extensions to the recently released AVX-512 ISA. We have evaluated the performance improvements enabled by FlexVec vectorization for 11 C/C++ SPEC 2006 benchmarks and 7 real applications with AVX-512 vectorization as baseline. We show that FlexVec vectorization technique produces a Geomean speedup of 9% for SPEC 2006 and a Geomean speedup of 11% for 7 real applications.

Cavity evolution and instability constraints of relativistic interiors

In this manuscript, we have identified the dynamical instability constraints of a self-gravitating cylindrical object within the framework of $f(R,T)$ theory of gravity. We have explored the modified field equations and corresponding dynamical equations for the systematic constructions of our analysis. We have imposed the linear perturbations on metric and material variables with some known static profile up to first order in the perturbation parameter. The role of expansion scalar is also examined in this scenario. The instability regimes have been discussed in the background of Newtonian and post-Newtonian limits. We found that the dark source terms due to the influence of modification in the gravity model is responsible for the instability of the system.

<em>Fin du Globe</em>: On Decadent Planets

As scholars across disciplines have turned their attention to the climate crisis, they have developed expanded critical frameworks—most notably, the Anthropocene—that aspire to understand a new planetary scale of human agency and to situate human history in relation to geological time. This essay argues that the literature of British decadence, which often contemplated the eventual ends of the planet and of the human species, offers resources for refining contemporary thought about planetary and temporal scale. Focusing on the Caribbean writer M. P. Shiel, the essay traces how decadent writing both reveals planetary scales to be irreducibly multiple and exposes a basic antinomy of scalar expansion: for decadents—as for us—to view the Earth and its history in their totality is also to witness their eventual disintegration.

LRS Bianchi type‐I string cosmological model in gravity

In this study the locally rotationally symmetric (LRS) Bianchi type‐I (BI) cosmological model has been investigated in the presence of one dimensional cosmic strings in gravity. The exact solutions of the field equations are obtained through the use of constant deceleration parameter and the scalar expansion is proportional to the shear scalar. Considering the accelerating nature of the universe in the present epoch, the physical behavior of the model has been discussed.

Minimally interacting holographic dark energy model in Bianchi type-III universe in Brans-Dicke theory

A spatially homogeneous and anisotropic Bianchi type-III universe filled with two minimally interacting fields is investigated: matter and holographic dark energy components in the framework of the Brans-Dicke (Phys. Rev. 124:925, 1961) theory of gravitation. To obtain determinate solutions of the field equations we have used (i) scalar expansion proportional to the shear scalar and (ii) special law of variation for Hubble’s parameter proposed by Berman (Nuovo Comento B 74:182, 1983). Some physical and kinematical properties of the model are also discussed.

Kantowski-Sachs bulk viscous string cosmological model in a scale covariant theory of gravitation

Spatially homogeneous and anisotropic Kantowski-Sachs space-time is considered in the scale covariant theory of gravitation proposed by Canuto et al. (Phys. Rev. Lett. 39:429, 1977) in the presence of bulk viscous fluid containing one dimensional cosmic strings. A determinate solution of the field equations of this theory is presented using the special law of variation proposed by Bermann (Nuovo Cimento B74:183, 1983). We have also used the proportionality of shear scalar to the scalar expansion of the space time. The solution obtained represents a bulk viscous string cosmological model in this theory. Some physical and kinematical properties of the model are also discussed.

Casimir Effect Near the Future Singularity in Kaluza Klein Viscous Cosmology

In this paper we investigate the analytical properties of the scalar expansion θ in the cosmic fluid close to the future singularity, when the fluid possesses a constant bulk viscosity ζ in the framework of Kaluza-Klein theory of gravitation. In addition, we assume the viscous cosmology theories in the sense that the Casimir contributions to the energy density and pressure are both proportional to 1/a 4, where a being scale factor. We also worked out the series expansion for the scalar expansion θ under the condition that the Casimir influence is small. However, near to the big rip singularity the Casimir term has to fade away and we obtain the same singularity behavior for the scalar expansion θ, energy density ρ, the scale factor a as in the Casimir-free viscous case.

Geodesic flows around charged black holes in two dimensions

We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the Raychaudhuri equation for expansion scalar as an initial value problem. The possibility of geodesic focusing/defocusing is then examined accordingly with different settings of black hole parameters. In view of the geodesic focusing/defocusing, the critical value of expansion scalar is also calculated in each case. The effect of the charge and the cosmological constant on the evolution of expansion scalar for timelike geodesics is discussed in detail.

Kaluza-Klein dark energy model in Brans-Dicke theory of gravitation

A five dimensional Kaluza-Klein dark energy model with a variable equation of state (EoS) parameter and a constant deceleration parameter is considered in the scalar-tensor theory proposed by Brans and Dicke (Phys. Rev. 24:925, 1961). We have introduced three different skew ness parameters along spatial directions which are time dependent. The field equations have been solved by using (i) the trace of the energy tensor of the fluid vanishes, (ii) shear scalar is proportional to scalar expansion and (iii) special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983). It is observed that in this case the EoS parameter turns out to be constant. Some physical and kinematical properties of the model obtained are also discussed.

Dynamics of relativistic fluids with structure scalars and $$\epsilon R^2$$ ϵ R 2 cosmology

This work is devoted to analyze the effects of $$f(R)$$ model on the dynamics of dissipative shearing viscous and anisotropic spherical matter configuration. In this framework, we develop scalar functions and link their expressions with various physical parameters and inflationary $$f(R)$$ dark source terms. We also relate the Weyl tensor as well as other matter variables with $$R+{\epsilon }R^2$$ background and obtain evolution equations for shear and expansion scalars. We conclude that structure scalars and $$f(R)$$ higher curvature terms have significant importance in the dynamics of self-gravitating systems.

Averaging in LRS class II spacetimes

We generalize Buchert’s averaged equations (Gen Relativ Gravit 32; 105, 2000; Gen Relativ Gravit 33; 1381, 2001) to LRS class II dust model in the sense that all Einstein equations are averaged, not only the trace part. We derive the relevant averaged equations and we investigate backreaction on expansion and shear scalars in an approximate LTB model. Finally we propose a way to close the system of averaged equations.

Evolution of geodesic congruences in a gravitationally collapsing scalar field background

The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation, and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity) in shaping the overall behavior of geodesic congruences.

Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold with interior boundary Σ. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show the existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on Σ, similar to those analyzed previously by Dain (2004 Class. Quantum Grav. 21 555–73), by Maxwell (2004, 2005 Commun. Math. Phys. 253 561–83), and by Holst and Tsogtgerel (2013 Class. Quantum Grav. 30 205011) as a model of black holes in various CMC settings, and by Holst et al (2013 Non-CMC solutions to the einstein constraint equations with apparent horizon boundaries arXiv:1310.2302v1) in the setting of far-from-CMC solutions on compact manifolds with boundary. These ‘marginally trapped surface’ Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region Σ are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assuming a suitable form of weak cosmic censorship, the results presented in this article guarantee the existence of initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new.

ChemInform Abstract: Thermal Expansion in C2/C Pyroxenes: A Review and New High‐Temperature Structural Data for a Pyroxene of Composition (Na0.53Ca0.47) (Al0.53Fe0.47)Si2O6 (Jd53Hd47)

AbstractReview: 40 refs.

Minimally interacting holographic Dark energy model in Brans-Dicke theory

In this paper, we have studied the anisotropic and homogeneous Bianchi type-V universe filled with two minimally interacting fields, matter and holographic dark energy components in the frame work of Brans and Dicke (Phys. Rev. 124:925, 1961) theory of gravitation. To obtain a determinate solution of the field equations we have used (i) the scalar expansion is proportional to the shear scalar and (ii) special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983). Some physical and kinematical properties of the model are also discussed.

Kantowski–Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization prescriptions

Using effective dynamics, we investigate the behavior of expansion and shear scalars in different proposed quantizations of the Kantowski–Sachs spacetime with matter in loop quantum cosmology. We find that out of the various proposed choices, there is only one known prescription which leads to the generic bounded behavior of these scalars. The bounds turn out to be universal and are determined by the underlying quantum geometry. This quantization is analogous to the so called ‘improved dynamics’ in the isotropic loop quantum cosmology, which is also the only one to respect the freedom of the rescaling of the fiducial cell at the level of effective spacetime description. Other proposed quantization prescriptions yield expansion and shear scalars which may not be bounded for certain initial conditions in effective dynamics. These prescriptions also have a limitation that the ‘quantum geometric effects’ can occur at an arbitrary scale. We show that the ‘improved dynamics’ of Kantowski–Sachs spacetime turns out to be a unique choice in a general class of possible quantization prescriptions, in the sense of leading to generic bounds on expansion and shear scalars and the associated physics being free from fiducial cell dependence. The behavior of the energy density in the ‘improved dynamics’ reveals some interesting features. Even without considering any details of the dynamical evolution, it is possible to rule out pancake singularities in this spacetime. The energy density is found to be dynamically bounded. These results show that the Planck scale physics of the loop quantized Kantowski–Sachs spacetime has key features common with the loop quantization of isotropic and Bianchi-I spacetimes.

Kantowski-Sachs Cosmological model with quark and strange quark matter in f(R) theory of gravity

Abstract In this paper we have studied the Kantowski- Sachs cosmological model with the quark and strange quark matter in the f (R) theory of gravity. The general solutions of the field equations are obtained by assuming the physical condition shear scalar σ is proportional to scalar expansion θ, which leads to the relation B = An between metric coefficients B and A. The physical and geometrical aspects of the model are also discussed.

Minimally interacting holographic dark energy model in a scalar- tensor theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-V universe filled with two minimally interacting fields; matter and holographic dark energy components is in investigated in the scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). To obtain a determinate solution of the field equations we have used the fact that the scalar expansion is proportional to the shear scalar. Some physical and kinematical properties of the model are also discussed.

LRS Bianchi Type-I Inflationary String Cosmological Model in Brans-Dicke Theory of Gravitation

We investigate locally rotational symmetric (LRS) Bianchi type I space time coupled with scalar field. String cosmological models generated by a cloud of strings with particles attached to them are studied in the Brans-Dicke theory. We assume that the expansion scalar is proportional to the shear scalar and also power law ansatz for scalar field. The physical behavior of the resulting model is discussed through different parameters.

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.