Dynamical spacetimes in conformal gravity

NASA Astrophysics Data System (ADS)

Zhang, Hongsheng; Zhang, Yi; Li, Xin-Zhou

2017-08-01

The conformal gravity remarkably boosts our prehension of gravity theories. We find a series of dynamical solutions in the W2-conformal gravity, including generalized Schwarzschild-Friedmann-Robertson-Walker (GSFRW), charged generalized Schwarzschild-Friedmann-Robertson-Walker (CGSFRW), especially rotating Friedmann-Robertson-Walker (RFRW), charged rotating Friedmann-Robertson-Walker (CRFRW), and a dynamical cylindrically symmetric solutions. The RFRW, CRFRW and the dynamical cylindrically symmetric solutions are never found in the Einstein gravity and modified gravities. The GSFRW and CGSFRW solutions take different forms from the corresponding solutions in the Einstein gravity.

Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haro, Jaume de, E-mail: jaime.haro@upc.edu

It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent waymore » to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.« less

Inflationary universe in deformed phase space scenario

NASA Astrophysics Data System (ADS)

Rasouli, S. M. M.; Saba, Nasim; Farhoudi, Mehrdad; Marto, João; Moniz, P. V.

2018-06-01

We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting herein proposed, produces entirely new consequences as summarized in what follows. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat Friedmann-Lemaî tre-Robertson-Walker (FLRW) universe, and while the Friedmann equation (Hamiltonian constraint) remains unaffected the Friedmann acceleration equation (and thus the Klein-Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. This last property is present either in the free field case or under the influence of the scalar field potentials considered here. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the R2 (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to obtain inflationary universe possessing the graceful exit when scalar field potentials are present.

Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann-Lemaître-Robertson-Walker spacetimes

NASA Astrophysics Data System (ADS)

Dai, Guowei; Romero, Alfonso; Torres, Pedro J.

2018-06-01

We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.

Self-similar cosmological solutions with dark energy. II. Black holes, naked singularities, and wormholes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maeda, Hideki; Department of Physics, International Christian University, 3-10-2 Osawa, Mitaka-shi, Tokyo 181-8585; Graduate School of Science and Engineering, Waseda University, Tokyo 169-8555

We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=({gamma}-1){mu} with 0<{gamma}<2/3. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they aremore » not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all nontraversable because of the absence of a past null infinity.« less

Why there is no Newtonian backreaction

NASA Astrophysics Data System (ADS)

Kaiser, Nick

2017-07-01

In the conventional framework for cosmological dynamics, the scalefactor a(t) is assumed to obey the 'background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations. It has recently been suggested that the emergence of structure modifies the evolution of a(t) via Newtonian (or 'kinematic') backreaction and that this may avoid the need for dark energy. Here, we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for a(t). The recently proposed modification of Rácz et al. does not reduce to Newtonian gravity in the limit of low velocities. We discuss the relation of this to the 'generalized Friedmann equation' of Buchert and Ehlers. These are quite different things; their formula describes individual regions and is obtained under the restrictive assumption that the matter behaves like a pressure-free fluid, whereas our result is exact for collisionless dynamics and is an auxiliary relation appearing in the structure equations. We use the symmetry of the general velocity autocorrelation function to show how Buchert's Q tends very rapidly to zero for large volume and that this does not simply arise 'by construction' through the adoption of periodic boundary conditions as has been claimed. We conclude that, to the extent that Newtonian gravity accurately describes the low-z universe, there is no backreaction of structure on a(t) and that the need for dark energy cannot be avoided in this way.

Statefinder diagnostic for modified Chaplygin gas cosmology in f(R,T) gravity with particle creation

NASA Astrophysics Data System (ADS)

Singh, J. K.; Nagpal, Ritika; Pacif, S. K. J.

In this paper, we have studied flat Friedmann-Lemaître-Robertson-Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state pm = Aρ ‑ B ργ, where 0 ≤ A ≤ 1, 0 ≤ γ ≤ 1 and B is any positive constant in f(R,T) gravity with particle creation. We have considered a simple parametrization of the Hubble parameter H in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the statefinder diagnostic pair {r,s} that characterizes the evolution of obtained models and explore their stability. The physical consequences of the models and their kinematic behaviors have also been scrutinized here in some detail.

Friedmann Cosmology with Matter Creation in Modified f( R, T) Gravity

NASA Astrophysics Data System (ADS)

Singh, Vijay; Singh, C. P.

2016-02-01

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f( R, T) ( R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f( R, T)= R+2 f( T) with "gamma-law" equation of state p = ( γ-1) ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3 β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bettoni, Dario; Liberati, Stefano, E-mail: dario@physics.technion.ac.il, E-mail: liberati@sissa.it

We present a general formulation of the theory for a non-minimally coupled perfect fluid in which both conformal and disformal couplings are present. We discuss how such non-minimal coupling is compatible with the assumptions of a perfect fluid and derive both the Einstein and the fluid equations for such model. We found that, while the Euler equation is significantly modified with the introduction of an extra force related to the local gradients of the curvature, the continuity equation is unaltered, thus allowing for the definition of conserved quantities along the fluid flow. As an application to cosmology and astrophysics wemore » compute the effects of the non-minimal coupling on a Friedmann-Lemaȋtre-Robertson-Walker metric at both background and linear perturbation level and on the Newtonian limit of our theory.« less

Inflation without inflaton: A model for dark energy

NASA Astrophysics Data System (ADS)

Falomir, H.; Gamboa, J.; Méndez, F.; Gondolo, P.

2017-10-01

The interaction between two initially causally disconnected regions of the Universe is studied using analogies of noncommutative quantum mechanics and the deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lemaître-Robertson-Walker (FLRW) metrics with scale factors a and b and cosmological constants Λa and Λb, respectively. The causality is turned on by positing a nontrivial Poisson bracket [Pα,Pβ]=ɛα βκ/G , where G is Newton's gravitational constant and κ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies, and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of κ . In this model, the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for κ ≪1 is also studied.

Cosmological singularity resolution from quantum gravity: The emergent-bouncing universe

NASA Astrophysics Data System (ADS)

Alesci, Emanuele; Botta, Gioele; Cianfrani, Francesco; Liberati, Stefano

2017-08-01

Alternative scenarios to the big bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so-called quantum reduced loop gravity) the Friedmann equations for cosmology are modified in such a way to replace the big bang singularity with a short bounce preceded by a metastable quantum phase in which the volume of the universe oscillates between a series of local maxima and minima. We call this hybrid scenario an "emergent-bouncing universe" since after a pure oscillating quantum phase the classical Friedmann spacetime emerges. Perspective developments and possible tests of this scenario are discussed in the end.

Future singularities and teleparallelism in loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bamba, Kazuharu; Haro, Jaume de; Odintsov, Sergei D., E-mail: bamba@kmi.nagoya-u.ac.jp, E-mail: jaime.haro@upc.edu, E-mail: odintsov@ieec.uab.es

2013-02-01

We demonstrate how holonomy corrections in loop quantum cosmology (LQC) prevent the Big Rip singularity by introducing a quadratic modification in terms of the energy density ρ in the Friedmann equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) space-time in a consistent and useful way. In addition, we investigate whether other kind of singularities like Type II,III and IV singularities survive or are avoided in LQC when the universe is filled by a barotropic fluid with the state equation P = −ρ−f(ρ), where P is the pressure and f(ρ) a function of ρ. It is shown that the Little Rip cosmology does notmore » happen in LQC. Nevertheless, the occurrence of the Pseudo-Rip cosmology, in which the phantom universe approaches the de Sitter one asymptotically, is established, and the corresponding example is presented. It is interesting that the disintegration of bound structures in the Pseudo-Rip cosmology in LQC always takes more time than that in Einstein cosmology. Our investigation on future singularities is generalized to that in modified teleparallel gravity, where LQC and Brane Cosmology in the Randall-Sundrum scenario are the best examples. It is remarkable that F(T) gravity may lead to all the kinds of future singularities including Little Rip.« less

Emergence of spacetime dynamics in entropy corrected and braneworld models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sheykhi, A.; Dehghani, M.H.; Hosseini, S.E., E-mail: asheykhi@shirazu.ac.ir, E-mail: mhd@shirazu.ac.ir, E-mail: elahehhosseini90@gmail.com

2013-04-01

A very interesting new proposal on the origin of the cosmic expansion was recently suggested by Padmanabhan [arXiv:1206.4916]. He argued that the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space drives the accelerated expansion of the universe, as well as the standard Friedmann equation through relation ΔV = Δt(N{sub sur}−N{sub bulk}). In this paper, we first present the general expression for the number of degrees of freedom on the holographic surface, N{sub sur}, using the general entropy corrected formula S = A/(4L{sub p}{sup 2})+s(A). Then, as two example, by applyingmore » the Padmanabhan's idea we extract the corresponding Friedmann equations in the presence of power-law and logarithmic correction terms in the entropy. We also extend the study to RS II and DGP braneworld models and derive successfully the correct form of the Friedmann equations in these theories. Our study further supports the viability of Padmanabhan's proposal.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomes, C.; Bertolami, O.; Rosa, J.G., E-mail: claudio.gomes@fc.up.pt, E-mail: joao.rosa@ua.pt, E-mail: orfeu.bertolami@fc.up.pt

We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions formore » some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.« less

Phase space of modified Gauss-Bonnet gravity.

PubMed

Carloni, Sante; Mimoso, José P

2017-01-01

We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f ( R ) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.

On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

The propagator W ( t 0 , t 1 )( g , h ) for the wave equation in a given space-time takes initial data ( g ( x ), h ( x )) on a Cauchy surface {( t , x ) :  t = t 0 } and evaluates the solution ( u ( t 1 , x ),∂ t u ( t 1 , x )) at other times t 1 . The Friedmann-Robertson-Walker space-times are defined for t 0 , t 1 >0, whereas for t 0 →0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K =0 and K =-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0< t 0 < t the limit, [Formula: see text] exists, it is independent of h ( x ), and for all reasonable initial data g ( x ), it gives rise to a well-defined solution for all t >0 emanating from the space-time singularity at t =0. Under reflection t →- t , the Friedmann-Robertson-Walker metric gives a space-time metric for t <0 with a singular future at t =0, and the same solution formulae hold. We thus have constructed solutions u ( t , x ) of the wave equation in Friedmann-Robertson-Walker space-times which exist for all [Formula: see text] and [Formula: see text], where in conformally regularized coordinates, these solutions are continuous through the singularity t =0 of space-time, taking on specified data u (0,⋅)= g (⋅) at the singular time.

Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes.

NASA Technical Reports Server (NTRS)

Morganstern, R. E.

1971-01-01

The Brans-Dicke cosmological equations for flat Friedmann-type expanding universes are solved parametrically for time, density, expansion parameter, and scalar field. These results reduce to a previously obtained exact solution to the radiation cosmology. Although the scalar field may be undetectable at the present epoch, it is felt that, if it exists, it must play an important role as one approaches the initial singularity of the cosmology.

On the asymptotic character of electromagnetic waves in a Friedmann Robertson Walker universe

NASA Astrophysics Data System (ADS)

Haghighipour, Nader

2005-02-01

Asymptotic properties of electromagnetic waves are studied within the context of Friedmann Robertson Walker (FRW) cosmology. Electromagnetic fields are considered as small perturbations on the background spacetime and Maxwell’s equations are solved for all three cases of flat, closed and open FRW universes. The asymptotic character of these solutions is investigated and their relevance to the problem of cosmological tails of electromagnetic waves is discussed.

Modified gravity in Arnowitt-Deser-Misner formalism

NASA Astrophysics Data System (ADS)

Gao, Changjun

2010-02-01

Motivated by Hořava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three-dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.

The Friedmann-Lemaître-Robertson-Walker Big Bang Singularities are Well Behaved

NASA Astrophysics Data System (ADS)

Stoica, Ovidiu Cristinel

2016-01-01

We show that the Big Bang singularity of the Friedmann-Lemaître-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Middleton, Chad A.; Stanley, Ethan

2011-10-15

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore » the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.« less

Dynamic wormhole solutions in Einstein-Cartan gravity

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Ziaie, Amir Hadi

2017-12-01

In the present work, we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory. The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.

A modified Friedmann equation

NASA Astrophysics Data System (ADS)

Ambjørn, J.; Watabiki, Y.

2017-12-01

We recently formulated a model of the universe based on an underlying W3-symmetry. It allows the creation of the universe from nothing and the creation of baby universes and wormholes for spacetimes of dimension 2, 3, 4, 6 and 10. Here we show that the classical large time and large space limit of these universes is one of exponential fast expansion without the need of a cosmological constant. Under a number of simplifying assumptions, our model predicts that w = ‑1.2 in the case of four-dimensional spacetime. The possibility of obtaining a w-value less than ‑1 is linked to the ability of our model to create baby universes and wormholes.

Cosmology from group field theory formalism for quantum gravity.

PubMed

Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo

2013-07-19

We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.

Electromagnetic fields in curved spacetimes

NASA Astrophysics Data System (ADS)

Tsagas, Christos G.

2005-01-01

We consider the evolution of electromagnetic fields in curved spacetimes and calculate the exact wave equations for the associated electric and magnetic components. Our analysis is fully covariant, applies to a general spacetime and isolates all the sources that affect the propagation of these waves. Among others, we explicitly show how the different components of the gravitational field act as driving sources of electromagnetic disturbances. When applied to perturbed Friedmann Robertson Walker cosmologies, our results argue for a superadiabatic-type amplification of large-scale cosmological magnetic fields in Friedmann models with open spatial curvature.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

NASA Astrophysics Data System (ADS)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

Constraining inverse-curvature gravity with supernovae.

PubMed

Mena, Olga; Santiago, José; Weller, Jochen

2006-02-03

We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07

Emergence of running dark energy from polynomial f( R) theory in Palatini formalism

NASA Astrophysics Data System (ADS)

Szydłowski, Marek; Stachowski, Aleksander; Borowiec, Andrzej

2017-09-01

We consider FRW cosmology in f(R)= R+ γ R^2+δ R^3 modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field and vanishing kinetic energy term. This potential determines the running cosmological constant term as a function of the Ricci scalar. As a result we obtain the emergent dark energy parametrization from the covariant theory. We study also singularities of the model and demonstrate that in the Einstein frame some undesirable singularities disappear.

Singularities in loop quantum cosmology.

PubMed

Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David

2008-12-19

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.

Self-similar perturbations of a Friedmann universe

NASA Technical Reports Server (NTRS)

Carr, Bernard J.; Yahil, Amos

1990-01-01

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

Cosmological implications of scalar field dark energy models in f(T,𝒯 ) gravity

NASA Astrophysics Data System (ADS)

Salako, Ines G.; Jawad, Abdul; Moradpour, Hooman

After reviewing the f(T,𝒯 ) gravity, in which T is the torsion scalar and 𝒯 is the trace of the energy-momentum tensor, we refer to two cosmological models of this theory in agreement with observational data. Thereinafter, we consider a flat Friedmann-Robertson-Walker (FRW) universe filled by a pressureless source and look at the terms other than the Einstein terms in the corresponding Friedmann equations, as the dark energy (DE) candidate. In addition, some cosmological features of models, including equation of states and deceleration parameters, are addressed helping us in getting the accelerated expansion of the universe in quintessence era. Finally, we extract the scalar field as well as potential of quintessence, tachyon, K-essence and dilatonic fields for both f(T,𝒯 ) models. It is observed that the dynamics of scalar field as well as the scalar potential of these models indicate an accelerated expanding universe in these models.

Light propagation in the averaged universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagheri, Samae; Schwarz, Dominik J., E-mail: s_bagheri@physik.uni-bielefeld.de, E-mail: dschwarz@physik.uni-bielefeld.de

Cosmic structures determine how light propagates through the Universe and consequently must be taken into account in the interpretation of observations. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of themore » null geodesic equation of motion. For the averaged geometry we then assume a flat Friedmann-Lemaître (FL) model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krasnov, Kirill; Shtanov, Yuri, E-mail: kirill.krasnov@nottingham.ac.uk, E-mail: shtanov@bitp.kiev.ua

We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energymore » density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity.« less

Holographic cosmology and phase transitions of SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Meyer, René; Toyoda, Fumihiko

2017-10-01

We study the time development of strongly coupled N =4 supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.

Towards the quantization of Eddington-inspired-Born-Infeld theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouhmadi-López, Mariam; Chen, Che-Yu, E-mail: mbl@ubi.pt, E-mail: b97202056@gmail.com

2016-11-01

The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantommore » perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity is expected to be avoided through the quantum approach within the EiBI theory.« less

Cosmological aspects of the Eisenhart-Duval lift

NASA Astrophysics Data System (ADS)

Cariglia, M.; Galajinsky, A.; Gibbons, G. W.; Horvathy, P. A.

2018-04-01

A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton-Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart-Duval framework is presented.

Conditions for defocusing around more general metrics in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Edholm, James

2018-04-01

Infinite derivative gravity is able to resolve the big bang curvature singularity present in general relativity by using a simplifying ansatz. We show that it can also avoid the Hawking-Penrose singularity, by allowing defocusing of null rays through the Raychaudhuri equation. This occurs not only in the minimal case where we ignore the matter contribution but also in the case where matter plays a key role. We investigate the conditions for defocusing for the general case where this ansatz applies and also for more specific metrics, including a general Friedmann-Robertson-Walker metric and three specific choices of the scale factor which produce a bouncing Friedmann-Robertson-Walker universe.

The varying cosmological constant: a new approximation to the Friedmann equations and universe model

NASA Astrophysics Data System (ADS)

Öztaş, Ahmet M.; Dil, Emre; Smith, Michael L.

2018-05-01

We investigate the time-dependent nature of the cosmological constant, Λ, of the Einstein Field Equation (EFE). Beginning with the Einstein-Hilbert action as our fundamental principle we develop a modified version of the EFE allowing the value of Λ to vary as a function of time, Λ(t), indirectly, for an expanding universe. We follow the evolving Λ presuming four-dimensional space-time and a flat universe geometry and present derivations of Λ(t) as functions of the Hubble constant, matter density, and volume changes which can be traced back to the radiation epoch. The models are more detailed descriptions of the Λ dependence on cosmological factors than previous, allowing calculations of the important parameters, Ωm and Ωr, to deep lookback times. Since we derive these without the need for extra dimensions or other special conditions our derivations are useful for model evaluation with astronomical data. This should aid resolution of several difficult problems of astronomy such as the best value for the Hubble constant at present and at recombination.

Misconceptions about an Expanding Universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samuel, Stuart; /SLAC /LBL, Berkeley

2005-12-14

Various results are obtained for a Friedmann-Robertson-Walker cosmology. We derive an exact equation that determines Hubble's law, clarify issues concerning the speeds of faraway objects and uncover a ''tail-light angle effect'' for distant luminous sources. The latter leads to a small, previously unnoticed correction to the parallax distance formula.

Bulk scalar field in brane-worlds with induced gravity inspired by the L(R) term

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari-Fard, M.; Sepangi, H.R., E-mail: heydarifard@qom.ac.ir, E-mail: hr-sepangi@sbu.ac.ir

2009-01-15

We obtain the effective field equations in a brane-world scenario within the framework of a DGP model where the action on the brane is an arbitrary function of the Ricci scalar, L(R), and the bulk action includes a scalar field in the matter Lagrangian. We obtain the Friedmann equations and acceleration conditions in the presence of the bulk scalar field for the R{sup n} term in four-dimensional gravity.

Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law

NASA Astrophysics Data System (ADS)

Abreu, Everton M. C.; Ananias Neto, Jorge; Mendes, Albert C. R.; Bonilla, Alexander

2018-02-01

In this work, we have illustrated the difference between both Tsallis and Kaniadakis entropies through cosmological models obtained from the formalism proposed by Padmanabhan, which is called holographic equipartition law. Similarly to the formalism proposed by Komatsu, we have obtained an extra driving constant term in the Friedmann equation if we deform the Tsallis entropy by Kaniadakis' formalism. We have considered initially Tsallis entropy as the black-hole (BH) area entropy. This constant term may lead the universe to be in an accelerated or decelerated mode. On the other hand, if we start with the Kaniadakis entropy as the BH area entropy and then by modifying the Kappa expression by Tsallis' formalism, the same absolute value but with opposite sign is obtained. In an opposite limit, no driving inflation term of the early universe was derived from both deformations.

Perturbative stability of SFT-based cosmological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galli, Federico; Koshelev, Alexey S., E-mail: fgalli@tena4.vub.ac.be, E-mail: alexey.koshelev@vub.ac.be

2011-05-01

We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numericallymore » that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.« less

Accelerated cosmos in a nonextensive setup

NASA Astrophysics Data System (ADS)

Moradpour, H.; Bonilla, Alexander; Abreu, Everton M. C.; Neto, Jorge Ananias

2017-12-01

Here we consider a flat FRW universe whose horizon entropy meets the Rényi entropy of nonextensive systems. In our model, the ordinary energy-momentum conservation law is not always valid. By applying the Clausius relation as well as the Cai-Kim temperature to the apparent horizon of a flat FRW universe, we obtain modified Friedmann equations. Fitting the model to the observational data on the current accelerated universe, some values for the model parameters are also addressed. Our study shows that the current accelerating phase of universe expansion may be described by a geometrical fluid, originated from the nonextensive aspects of geometry, which models a varying dark energy source interacting with the matter field in the Rastall way. Moreover, our results indicate that the probable nonextensive features of spacetime may also be used to model a varying dark energy source which does not interact with the matter field and is compatible with the current accelerated phase of the Universe.

Cosmology on a cosmic ring

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niedermann, Florian; Schneider, Robert, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de

We derive the modified Friedmann equations for a generalization of the Dvali-Gabadadze-Porrati (DGP) model in which the brane has one additional compact dimension. The main new feature is the emission of gravitational waves into the bulk. We study two classes of solutions: first, if the compact dimension is stabilized, the waves vanish and one exactly recovers DGP cosmology. However, a stabilization by means of physical matter is not possible for a tension-dominated brane, thus implying a late time modification of 4D cosmology different from DGP. Second, for a freely expanding compact direction, we find exact attractor solutions with zero 4Dmore » Hubble parameter despite the presence of a 4D cosmological constant. The model hence constitutes an explicit example of dynamical degravitation at the full nonlinear level. Without stabilization, however, there is no 4D regime and the model is ruled out observationally, as we demonstrate explicitly by comparing to supernova data.« less

An exposition on Friedmann cosmology with negative energy densities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nemiroff, Robert J.; Joshi, Ravi; Patla, Bijunath R., E-mail: nemiroff@mtu.edu, E-mail: rjoshimtu@gmail.com, E-mail: bijunath.patla@nist.gov

2015-06-01

How would negative energy density affect a classic Friedmann cosmology? Although never measured and possibly unphysical, certain realizations of quantum field theories leaves the door open for such a possibility. In this paper we analyze the evolution of a universe comprising varying amounts of negative energy forms. Negative energy components have negative normalized energy densities, Ω < 0. They include negative phantom energy with an equation of state parameter w < −1, negative cosmological constant: w=−1, negative domain walls: w = −2/3, negative cosmic strings: w=−1/3, negative mass: w = 0, negative radiation: w = 1/3 and negative ultralight: w > 1/3. Assuming that such energy forms generate pressure like perfect fluids,more » the attractive or repulsive nature of negative energy components are reviewed. The Friedmann equation is satisfied only when negative energy forms are coupled to a greater magnitude of positive energy forms or positive curvature. We show that the solutions exhibit cyclic evolution with bounces and turnovers.The future and fate of such universes in terms of curvature, temperature, acceleration, and energy density are reviewed. The end states are dubbed ''big crunch,' '' big void,' or ''big rip' and further qualified as ''warped',''curved', or ''flat',''hot' versus ''cold', ''accelerating' versus ''decelerating' versus ''coasting'. A universe that ends by contracting to zero energy density is termed ''big poof.' Which contracting universes ''bounce' in expansion and which expanding universes ''turnover' into contraction are also reviewed.« less

Newton's laws of motion in the form of a Riccati equation.

PubMed

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

An instability of the standard model of cosmology creates the anomalous acceleration without dark energy

NASA Astrophysics Data System (ADS)

Smoller, Joel; Temple, Blake; Vogler, Zeke

2017-11-01

We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein's original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p=0. In this phase portrait, the critical k=0 Friedmann space-time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space-time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space-times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein's original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

An instability of the standard model of cosmology creates the anomalous acceleration without dark energy.

PubMed

Smoller, Joel; Temple, Blake; Vogler, Zeke

2017-11-01

We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein's original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p =0. In this phase portrait, the critical k =0 Friedmann space-time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space-time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space-times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein's original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

Induced gravity on intersecting brane worlds. II. Cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corradini, Olindo; Koyama, Kazuya; Tasinato, Gianmassimo

2008-12-15

We explore cosmology of intersecting brane worlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension-one brane and a codimension-two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six-dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension-two brane at the intersection and we discuss their features.

Exact Cosmological Models with Yang–Mills Fields on Lyra Manifold

NASA Astrophysics Data System (ADS)

Shchigolev, V. K.; Bezbatko, D. N.

2018-04-01

The present study deals with the Friedmann-Robertson-Walker cosmological models with Yang-Mills (YM) fields in Lyra geometry. The energy-momentum tensor of the YM fields for our models is obtained with the help of an exact solution to the YM equations with minimal coupling to gravity. Two specific exact solutions of the model are obtained regarding the effective equation of state and the exponential law of expansion. The physical and geometric behavior of the model is also discussed.

Noether symmetries and stability of ideal gas solutions in Galileon cosmology

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Jamal, Sameerah; Leon, Genly; Paliathanasis, Andronikos

2017-03-01

A class of generalized Galileon cosmological models, which can be described by a pointlike Lagrangian, is considered in order to utilize Noether's theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Because of the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

The cosmological model with a wormhole and Hawking temperature near apparent horizon

NASA Astrophysics Data System (ADS)

Kim, Sung-Won

2018-05-01

In this paper, a cosmological model with an isotropic form of the Morris-Thorne type wormhole was derived in a similar way to the McVittie solution to the black hole in the expanding universe. By solving Einstein's field equation with plausible matter distribution, we found the exact solution of the wormhole embedded in Friedmann-Lemaître-Robertson-Walker universe. We also found the apparent cosmological horizons from the redefined metric and analyzed the geometric natures, including causal and dynamic structures. The Hawking temperature for thermal radiation was obtained by the WKB approximation using the Hamilton-Jacobi equation and Hamilton's equation, near the apparent cosmological horizon.

On a remarkable electromagnetic field in the Einstein Universe

NASA Astrophysics Data System (ADS)

Kopiński, Jarosław; Natário, José

2017-06-01

We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the 3-sphere S^3. The conformal equivalence between Minkowski's spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.

Polynomial f (R ) Palatini cosmology: Dynamical system approach

NASA Astrophysics Data System (ADS)

Szydłowski, Marek; Stachowski, Aleksander

2018-05-01

We investigate cosmological dynamics based on f (R ) gravity in the Palatini formulation. In this study, we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piecewise smooth dynamical system. This system is reduced to a 2D dynamical system of the Newtonian type. We demonstrate how the trajectories can be sewn to guarantee C0 extendibility of the metric similarly as "Milne-like" Friedmann-Lemaître-Robertson-Walker spacetimes are C0-extendible. We point out that importance of the dynamical system of the Newtonian type with nonsmooth right-hand sides in the context of Palatini cosmology. In this framework, we can investigate singularities which appear in the past and future of the cosmic evolution. We consider cosmological systems in both Einstein and Jordan frames. We show that at each frame the topological structures of phase space are different.

The Jungle Universe: coupled cosmological models in a Lotka-Volterra framework

NASA Astrophysics Data System (ADS)

Perez, Jérôme; Füzfa, André; Carletti, Timoteo; Mélot, Laurence; Guedezounme, Lazare

2014-06-01

In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaître universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaître cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserves the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.

FLRW cosmological models with quark and strange quark matters in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Nagpal, Ritika; Singh, J. K.; Aygün, S.

2018-06-01

In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of f(R,T) gravity in the background of Friedmann-Lemaître-Robertson-Walker (FLRW) metric. To get exact solutions of modified field equations we have used f(R,T ) = R + 2 f(T) model given by Harko et al. with two different parametrization of geometrical parameters i.e. the parametrization of the deceleration parameter q , and the scale factor a in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in f(R,T) gravity and General Relativity (GR). All models in f(R,T) gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Aktaş and Aygün in f(R,T) gravity. However, we have also discussed the physical consequences of our obtained models.

Solutions to horava gravity.

PubMed

Lü, H; Mei, Jianwei; Pope, C N

2009-08-28

Recently Horava proposed a nonrelativistic renormalizable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this Letter, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain solutions for the Friedmann-Lemaître-Robertson-Walker cosmological metric.

Disformally self-tuning gravity

NASA Astrophysics Data System (ADS)

Emond, William T.; Saffin, Paul M.

2016-03-01

We extend a previous self-tuning analysis of the most general scalar-tensor theory of gravity in four dimensions with second order field equations by considering a generalized coupling to the matter sector. Through allowing a disformal coupling to matter we are able to extend the Fab Four model and construct a new class of theories that are able to tune away the cosmological constant on Friedmann-Lemaitre-Robertson-Walker backgrounds.

Emergence of spaces and the dynamic equations of FRW universes in the f(R) theory and deformed Hořava-Lifshitz theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tu, Fei-Quan; Chen, Yi-Xin, E-mail: fqtuzju@foxmail.com, E-mail: yxchen@zimp.zju.edu.cn

It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed Hořava-Lifshitz(HL) theory.

A NOTE ON THE UNIFIED FIRST LAW IN f(R) GRAVITY THEORY

NASA Astrophysics Data System (ADS)

Zhang, Yi; Gong, Yungui; Zhu, Zong-Hong

2012-04-01

Because of the dynamical equivalence between the f(R) gravity and the Brans-Dicke theory, the dynamical equation in the f(R) gravity is suggested to be derived from a view point of thermodynamics here. By a conformal transformation, the Brans-Dicke theory in the Jordan frame could be expressed as a minimal coupling scalar field theory in Einstein frame. Using the entropy-area relation d˜ {S} = d˜ {A}/4 G, the correct Friedmann equations could be gotten in both frames. Furthermore, we also discuss the corresponding generalized Misner-Sharp energies for theoretical consistence.

The spectrum of density perturbations in an expanding universe

NASA Technical Reports Server (NTRS)

Silk, J.

1974-01-01

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

Loop quantum cosmology with self-dual variables

NASA Astrophysics Data System (ADS)

Wilson-Ewing, Edward

2015-12-01

Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann space-time coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomylike operators of which some are well defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived which provide a good approximation to the full quantum dynamics for sharply peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a nonsingular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.

Bouncing cosmologies from quantum gravity condensates

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward

2017-02-01

We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

Standard cosmology delayed

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choudhury, Debajyoti; Ghoshal, Debashis; Sen, Anjan Ananda, E-mail: debajyoti.choudhury@gmail.com, E-mail: dghoshal@mail.jnu.ac.in, E-mail: anjan.ctp@jmi.ac.in

2012-02-01

The introduction of a delay in the Friedmann equation of cosmological evolution is shown to result in the very early universe undergoing the necessary accelerated expansion in the usual radiation (or matter) dominated phase. Occurring even without a violation of the strong energy condition, this expansion slows down naturally to go over to the decelerated phase, namely the standard Hubble expansion. This may obviate the need for a scalar field driven inflationary epoch.

Improved treatment of optics in the Lindquist-Wheeler models

NASA Astrophysics Data System (ADS)

Clifton, Timothy; Ferreira, Pedro G.; O'Donnell, Kane

2012-01-01

We consider the optical properties of Lindquist-Wheeler (LW) models of the Universe. These models consist of lattices constructed from regularly arranged discrete masses. They are akin to the Wigner-Seitz construction of solid state physics, and result in a dynamical description of the large-scale Universe in which the global expansion is given by a Friedmann-like equation. We show that if these models are constructed in a particular way then the redshifts of distant objects, as well as the dynamics of the global space-time, can be made to be in good agreement with the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) solutions of Einstein’s equations, at the level of ≲3% out to z≃2. Angular diameter and luminosity distances, on the other hand, differ from those found in the corresponding FLRW models, while being consistent with the “empty beam” approximation, together with the shearing effects due to the nearest masses. This can be compared with the large deviations found from the corresponding FLRW values obtained in a previous study that considered LW models constructed in a different way. We therefore advocate the improved LW models we consider here as useful constructions that appear to faithfully reproduce both the dynamical and observational properties of space-times containing discrete masses.

Study of thermodynamic laws in f(R,T,R{sub μν}T{sup μν}) gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharif, M.; Zubair, M., E-mail: msharif.math@pu.edu.pk, E-mail: mzubairkk@gmail.com

2013-11-01

We study first and second laws of black hole thermodynamics at the apparent horizon of FRW spacetime in f(R,T,R{sub μν}T{sup μν}) gravity, where R, R{sub μν} are the Ricci scalar and Riemann tensor and T is the trace of the energy-momentum tensor T{sub μν}. We develop the Friedmann equations for any spatial curvature in this modified theory and show that these equations can be transformed to the form of Clausius relation T{sub h}S{sub eff} = δQ. Here T{sub h} is the horizon temperature, S{sub eff} is the entropy which contains contributions both from horizon entropy and additional entropy term introducedmore » due to the non-equilibrating description and δQ is the energy flux across the horizon. The generalized second law of thermodynamics is also established in a more comprehensive form and one can recover the corresponding results in Einstein, f(R) and f(R,T) gravities. We discuss GSLT in the locality of assumption that temperature of matter inside the horizon is similar to that of horizon. Finally, we consider particular models in this theory and generate constraints on the coupling parameter for the validity of GSLT.« less

Alexander A Friedmann

NASA Astrophysics Data System (ADS)

Tropp, Eduard A.; Frenkel, Viktor Ya.; Chernin, Artur D.; Dron, Alexander; Burov, Michael

2006-05-01

Preface; 1. The Friedmanns and the Vojaceks; 2. At the 2nd St Petersburg Gymnasium; 3. University years, 1906-14; 4. In search of a way; 5. War years; 6. Moscow - Perm - Petrograd; 7. Theoretical department of the Main Geophysical Observatory; 8. Space and time; 9. Geometry and dynamics of the Universe; 10. Petrograd, 1920-4; 11. The final year; 12. Friedmann's world; Conclusion; Main dates in Friedmann's life and work; Bibliography; Name Index.

Testing cosmology from fundamental considerations: Is the Friedmann universe intrinsically flat

NASA Astrophysics Data System (ADS)

Mitra, Abhas

2014-02-01

Recently Melia and Shevchuk (Mon Not R Astron Soc 419:2579,2012) (MS) have proposed the so-called cosmology where the "Gravitational Horizon" of the universe is equal to the distance travelled by light since "Big Bang". Here we would like to see whether the basic claim is correct or not because MS have not given any cogent derivation for the same. Essentially we will compare the twin expressions for the Einstein energy momentum complex (EMC) of the Friedmann universe obtained by using an appropriate superpotential and also by a direct method. To enable a meaningful comparison of the twin expressions, both are computed by using the same quasi-Cartesian coordinates. We however do not claim that Einstein EMC is superior to many other routes of defining EM of a self-gravitating system. In fact, for static isolated spherical syatems, the idea of a coordinate independent field energy of Lynden-Bell and Katz (Mon Not R Astron Soc 213:21, 1985) might be quite physically significant. Yet, here, we use Einstein EMC because (i) our system is non-static and not isolated one (ii) our primary aim is not find any absolute value of EM, and, finally, (iii) only Einstein pseudo-tensor offers equivalent twin expressions for EM which one can be equated irrespective of any physical significance. Following such comparison of equivalent twin expressions of Einstein energy, we find an exact proof as to why Friedmann universe must be spatially flat even though, mathematically one can conceive of curved spaces in any dimension. Additionally, it follows that, apparently, the scale factor as insisted by proposition. Nonetheless, because of close similarity of this form, , with the (vacuum) Milne metric, and also because of implied unphysical equation of state, cosmology is unlikely to represent the physical universe.

Evolution of Cosmology

NASA Astrophysics Data System (ADS)

Ross, Charles H.

2005-04-01

Aristotle thought that the universe was finite and Earth centered. Newton thought that it was infinite. Einstein guessed that the universe was finite, spherical, static, warped, and closed. Hubble's 1930 discovery of the expanding universe, Penzias and Wilson's 1968 discovery of the isotropic CMB, and measurements on light element abundances, however, established a big bang origin. Vera Rubin's 1980 dark matter discovery significantly impacted contending theories. However, 1998 is the year when sufficiently accurate supernova and primordial deuterium data was available to truly explore the universe. CMB anisotropy measurements further extended our cosmological database in 2003. On the theoretical side, Friedmann's 1922 perturbation solution of Einstein's general relativity equations for a static universe has shaped the thought and direction in cosmology for the past 80 years. It describes 3D space as a dynamic function of time. However, 80 years of trying to fit Friedmann's solution to observational data has been a bumpy road - resulting in such counter-intuitive, but necessary, features as rapid inflation, precision tuning, esoteric dark matter, and an accelerating input of esoteric dark energy.

f(R)-gravity from Killing tensors

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos

2016-04-01

We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.

Celestial ephemerides in an expanding universe

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.

2012-09-01

The post-Newtonian theory of motion of celestial bodies and propagation of light was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the Solar System with unparalleled precision. The cornerstone of the theory is the postulate that the Solar System is gravitationally isolated from the rest of the Universe and the background spacetime is asymptotically flat. The present article extends this theoretical concept and formulates the principles of celestial dynamics of particles and light moving in the gravitational field of a localized astronomical system embedded to the expanding Friedmann-Lemaître-Robertson-Walker universe. We formulate the precise mathematical concept of the Newtonian limit of Einstein’s field equations in the conformally flat Friedmann-Lemaître-Robertson-Walker spacetime and analyze the geodesic motion of massive particles and light in this limit. We prove that by doing conformal spacetime transformations, one can reduce the equations of motion of particles and light to the classical form of the Newtonian theory. However, the time arguments in the equations of motion of particles and light differ from each other in terms being proportional to the Hubble constant H. This leads to the important conclusion that the equations of light propagation used currently by space navigation centers for fitting range and Doppler-tracking observations of celestial bodies are missing some terms of the cosmological origin that are proportional to the Hubble constant H. We also analyze the effect of the cosmological expansion on motion of electrons in atoms. We prove that the Hubble expansion does not affect the atomic frequencies and hence does not affect the atomic time scale used in the creation of astronomical ephemerides. We derive the cosmological correction to the light travel time equation and argue that its measurement opens an exciting opportunity to determine the local value of the Hubble constant H in the Solar System independently of cosmological observations.

Equivalent off-diagonal cosmological models and ekpyrotic scenarios in -modified, massive, and einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2015-04-01

We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and -modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlevé-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed.

New holographic dark energy model inspired by the DGP braneworld

NASA Astrophysics Data System (ADS)

Sheykhi, A.; Dehghani, M. H.; Ghaffari, S.

2016-11-01

The energy density of the holographic dark energy (HDE) is based on the area law of entropy, and thus any modification of the area law leads to a modified holographic energy density. Inspired by the entropy expression associated with the apparent horizon of a Friedmann-Robertson-Walker (FRW) universe in DGP braneworld, we propose a new model for the HDE in the framework of DGP brane cosmology. We investigate the cosmological consequences of this new model and calculate the equation of state (EoS) parameter by choosing the Hubble radius, L = H-1, as the system’s IR cutoff. Our study show that, due to the effects of the extra dimension (bulk), the identification of IR cutoff with Hubble radius, can reproduce the present acceleration of the universe expansion. This is in contrast to the ordinary HDE in standard cosmology which leads to the zero EoS parameter in the case of choosing the Hubble radius as system’s IR cutoff in the absence of interaction between dark matter (DM) and dark energy (DE).

k-essence in the DGP brane-world cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouhmadi-Lopez, Mariam; Chimento, Luis P.

We analyze a Dvali-Gabadadze-Porrati (DGP) brane filled with a k-essence field and assume the k field evolving linearly with the cosmic time of the brane. We then solve analytically the Friedmann equation and deduce the different behavior of the brane at the low- and the high-energy regimes. The asymptotic behavior can be quite different involving accelerating branes, big bangs, big crunches, big rips, or quiescent singularities. The latter correspond to a type of sudden singularity.

General Relativity

NASA Astrophysics Data System (ADS)

Hobson, M. P.; Efstathiou, G. P.; Lasenby, A. N.

2006-02-01

1. The spacetime of special relativity; 2. Manifolds and coordinates; 3. Vector calculus on manifolds; 4. Tensor calculus on manifolds; 5. Special relativity revisited; 6. Electromagnetism; 7. The equivalence principle and spacetime curvature; 8. The gravitational field equations; 9. The Schwarzschild geometry; 10. Experimental tests of general relativity; 11. Schwarzschild black holes; 12. Further spherically-symmetric geometries; 13. The Kerr geometry; 14. The Friedmann-Robertson-Walker geometry; 15. Cosmological models; 16. Inflationary cosmology; 17. Linearised general relativity; 18. Gravitational waves; 19. A variational approach to general relativity.

On the cosmology of scalar-tensor-vector gravity theory

NASA Astrophysics Data System (ADS)

Jamali, Sara; Roshan, Mahmood; Amendola, Luca

2018-01-01

We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and μ(x), and one vector field phiα(x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θs, in MOG. We find that 8× 10‑3rad<θs<8.2× 10‑3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.

Cosmological perturbations in the entangled inflationary universe

NASA Astrophysics Data System (ADS)

Robles-Pérez, Salvador J.

2018-03-01

In this paper, the model of a multiverse made up of universes that are created in entangled pairs that conserve the total momentum conjugated to the scale factor is presented. For the background spacetime, assumed is a Friedmann-Robertson-Walker metric with a scalar field with mass m minimally coupled to gravity. For the fields that propagate in the entangled spacetimes, the perturbations of the spacetime and the scalar field, whose quantum states become entangled too, are considered. They turn out to be in a quasithermal state, and the corresponding thermodynamical magnitudes are computed. Three observables are expected to be caused by the creation of the universes in entangled pairs: a modification of the Friedmann equation because of the entanglement of the spacetimes, a modification of the effective value of the potential of the scalar field by the backreaction of the perturbation modes, and a modification of the spectrum of fluctuations because the thermal distribution is induced by the entanglement of the partner universes. The later would be a distinctive feature of the creation of universes in entangled pairs.

Interacting parametrized post-Friedmann method

NASA Astrophysics Data System (ADS)

Richarte, Martín G.; Xu, Lixin

2016-04-01

We apply the interacting parametrized post-Friedmann (IPPF) method to coupled dark energy models where the interaction is proportional to dark matter density at background level. In the first case, the dark components are treated as fluids and the growth of dark matter perturbations only feel the interaction via the modification of background quantities provided dark matter follows geodesic. We also perform a Markov Chain Monte-Carlo analysis which combines several cosmological probes including the cosmic microwave background (WMAP9+Planck) data, baryon acoustic oscillation (BAO) measurements, JLA sample of supernovae, Hubble constant (HST), and redshift-space distortion (RSD) measurements through the fσ 8(z) data points. The joint observational analysis of Planck+WP+JLA+BAO+HST+ RSD data leads to a coupling parameter, ξ c=0.00140_{-0.00080}^{+0.00079} at 1σ level for vanishing momentum transfer potential. On the other hand, we deal with a coupled quintessence model which exhibits a violation of the equivalence principle coming form a coupling term in the modified Euler equation; as a result of that the local Hubble expansion rate and the effective gravitational coupling are both enhanced. Provided that the interaction is parallel to scalar field velocity the momentum transfer potential is switched on, leading to a lower interaction coupling ξ c=0.00136_{-0.00073}^{+0.00080} at 1σ level when Planck+WP+JLA+BAO+HST+RSD data are combined. Besides, the CMB power spectrum shows up a correlation between the coupling parameter ξ c and the position of acoustic peaks or their amplitudes. The first peak's height increases when ξ c takes larger values and its position is shifted. We also obtain the matter power spectrum may be affected by the strength of interaction coupling over scales bigger than 10^{-2} h Mpc^{-1}, reducing its amplitude in relation to the vanilla model.

FLRW Cosmology from Yang-Mills Gravity with Translational Gauge Symmetry

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-03-01

We extend to basic cosmology the subject of Yang-Mills gravity — a theory of gravity based on local translational gauge invariance in flat space-time. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of general relativity (GR). The assumption that this "effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedmann equations are derived and then solved in closed form for the three special cases of a universe dominated by (1) matter, (2) radiation and (3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.

Oscillations and Rolling for Duffing's Equation

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Piskovskiy, E. V.; Volovich, I. V.

2013-01-01

The Duffing equation has been used to model nonlinear dynamics not only in mechanics and electronics but also in biology and in neurology for the brain process modeling. Van der Pol's method is often used in nonlinear dynamics to improve perturbation theory results when describing small oscillations. However, in some other problems of nonlinear dynamics particularly in case of Duffing-Higgs equation in field theory, for the Einsten-Friedmann equations in cosmology and for relaxation processes in neurology not only small oscillations regime is of interest but also the regime of slow rolling. In the present work a method for approximate solution to nonlinear dynamics equations in the rolling regime is developed. It is shown that in order to improve perturbation theory in the rolling regime it turns out to be effective to use an expansion in hyperbolic functions instead of trigonometric functions as it is done in van der Pol's method in case of small oscillations. In particular the Duffing equation in the rolling regime is investigated using solution expressed in terms of elliptic functions. Accuracy of obtained approximation is estimated. The Duffing equation with dissipation is also considered.

Alexander A Friedmann

NASA Astrophysics Data System (ADS)

Tropp, Eduard A.; Frenkel, Viktor Ya.; Chernin, Artur D.

1993-06-01

Our universe can be described mathematically by a simple model developed in 1922 at Petrograd (St. Petersburg) by Alexander Friedmann (1888-1925). Without the benefit of observational evidence, Friedmann predicted that the whole universe would expand and evolve with time. This astonishing prediction was confirmed seven years later by Edwin Hubble. Its originator, unfortunately didn't live to savor this triumph. This vivid biography of an outstanding scientist sets his life and work against a wide backdrop of the history of cosmological studies and its major players, such as Einstein and others. The book is a window on Friedmann's school and university years, military service, and teaching and research during a seminal period of Soviet history. The authors include unique archival material, such as Friedmann's letters from the Russian Front, as well as contemporary records and reminiscences of colleagues. There is a detailed treatment of his work in theoretical cosmology (1922-1924), set in the context of the organization of Soviet science at the time.

Stability and Hamiltonian formulation of higher derivative theories

NASA Astrophysics Data System (ADS)

Schmidt, Hans-Jürgen

1994-06-01

We analyze the presuppositions leading to instabilities in theories of order higher than second. The type of fourth-order gravity which leads to an inflationary (quasi-de Sitter) period of cosmic evolution by inclusion of one curvature-squared term (i.e., the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler-DeWitt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler-DeWitt equation for a spatially flat Friedmann model and L=R2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth-order gravity to second order.

The wave equation in Friedmann-Robertson-Walker space-times and asymptotics of the intensity and distance relationship of a localised source

NASA Astrophysics Data System (ADS)

Starko, Darij; Craig, Walter

2018-04-01

Variations in redshift measurements of Type 1a supernovae and intensity observations from large sky surveys are an indicator of a component of acceleration in the rate of expansion of space-time. A key factor in the measurements is the intensity-distance relation for Maxwell's equations in Friedmann-Robertson-Walker (FRW) space-times. In view of future measurements of the decay of other fields on astronomical time and spatial scales, we determine the asymptotic behavior of the intensity-distance relationship for the solution of the wave equation in space-times with an FRW metric. This builds on previous work done on initial value problems for the wave equation in FRW space-time [Abbasi, B. and Craig, W., Proc. R. Soc. London, Ser. A 470, 20140361 (2014)]. In this paper, we focus on the precise intensity decay rates of the special cases for curvature k = 0 and k = -1, as well as giving a general derivation of the wave solution for -∞ < k < 0. We choose a Cauchy surface {(t, x) : t = t0 > 0} where t0 represents the time of an initial emission source, relative to the Big Bang singularity at t = 0. The initial data [g(x), h(x)] are assumed to be compactly supported; supp(g, h) ⊆ BR(0) and terms in the expression for the fundamental solution for the wave equation with the slowest decay rate are retained. The intensities calculated for coordinate time {t : t > 0} contain correction terms proportional to the ratio of t0 and the time differences ρ = t - t0. For the case of general curvature k, these expressions for the intensity reduce by scaling to the same form as for k = -1, from which we deduce the general formula. We note that for typical astronomical events such as Type 1a supernovae, the first order correction term for all curvatures -∞ < k < 0 is on the order of 10-4 smaller than the zeroth order term. These correction terms are small but may be significant in applications to alternative observations of cosmological space-time expansion rates.

Global cosmological dynamics for the scalar field representation of the modified Chaplygin gas

NASA Astrophysics Data System (ADS)

Uggla, Claes

2013-09-01

In this paper we investigate the global dynamics for the minimally coupled scalar field representation of the modified Chaplygin gas in the context of flat Friedmann-Lemaître-Robertson Walker cosmology. The tool for doing this is a new set of bounded variables that lead to a regular dynamical system. It is shown that the exact modified Chaplygin gas perfect fluid solution appears as a straight line in the associated phase plane. It is also shown that no other solutions stay close to this solution during their entire temporal evolution, but that there exists an open subset of solutions that stay arbitrarily close during an intermediate time interval, and into the future in the case when the scalar field potential exhibits a global minimum.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pereira, S.H.; Pinho, A.S.S.; Silva, J.M. Hoff da

In this work the exact Friedmann-Robertson-Walker equations for an Elko spinor field coupled to gravity in an Einstein-Cartan framework are presented. The torsion functions coupling the Elko field spin-connection to gravity can be exactly solved and the FRW equations for the system assume a relatively simple form. In the limit of a slowly varying Elko spinor field there is a relevant contribution to the field equations acting exactly as a time varying cosmological model Λ( t )=Λ{sub *}+3β H {sup 2}, where Λ{sub *} and β are constants. Observational data using distance luminosity from magnitudes of supernovae constraint the parametersmore » Ω {sub m} and β, which leads to a lower limit to the Elko mass. Such model mimics, then, the effects of a dark energy fluid, here sourced by the Elko spinor field. The density perturbations in the linear regime were also studied in the pseudo-Newtonian formalism.« less

Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

NASA Astrophysics Data System (ADS)

Kumar, Suresh; Xu, Lixin

2014-10-01

In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann-Robertson-Walker space-time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components are described by Chevallier-Polarski-Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch.

Bouncing and emergent cosmologies from Arnowitt–Deser–Misner RG flows

NASA Astrophysics Data System (ADS)

Bonanno, Alfio; Gionti, S. J. Gabriele; Platania, Alessia

2018-03-01

Asymptotically safe gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton’s coupling are functions of the energy scale whose evolution is dictated by the renormalization group (RG) equations. The formulation of the RG equations on foliated spacetimes, based on the Arnowitt–Deser–Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the Laplacian operator on the spatial slices. Combining this idea with an RG improvement procedure, in this work we study quantum gravitational corrections to the Einstein–Hilbert action on Friedmann–Lemaître–Robertson–Walker backgrounds. The resulting quantum-corrected Friedmann equations can give rise to both bouncing cosmologies and emergent Universe solutions. Our bouncing models do not require the presence of exotic matter and emergent Universe solutions can be constructed for any allowed topology of the spatial slices.

Dark energy models through nonextensive Tsallis' statistics

NASA Astrophysics Data System (ADS)

Barboza, Edésio M.; Nunes, Rafael da C.; Abreu, Everton M. C.; Ananias Neto, Jorge

2015-10-01

The accelerated expansion of the Universe is one of the greatest challenges of modern physics. One candidate to explain this phenomenon is a new field called dark energy. In this work we have used the Tsallis nonextensive statistical formulation of the Friedmann equation to explore the Barboza-Alcaniz and Chevalier-Polarski-Linder parametric dark energy models and the Wang-Meng and Dalal vacuum decay models. After that, we have discussed the observational tests and the constraints concerning the Tsallis nonextensive parameter. Finally, we have described the dark energy physics through the role of the q-parameter.

Numerical approach to model independently reconstruct f (R ) functions through cosmographic data

NASA Astrophysics Data System (ADS)

Pizza, Liberato

2015-06-01

The challenging issue of determining the correct f (R ) among several possibilities is revised here by means of numerical reconstructions of the modified Friedmann equations around the redshift interval z ∈[0 ,1 ] . Frequently, a severe degeneracy between f (R ) approaches occurs, since different paradigms correctly explain present time dynamics. To set the initial conditions on the f (R ) functions, we involve the use of the so-called cosmography of the Universe, i.e., the technique of fixing constraints on the observable Universe by comparing expanded observables with current data. This powerful approach is essentially model independent, and correspondingly we got a model-independent reconstruction of f (R (z )) classes within the interval z ∈[0 ,1 ]. To allow the Hubble rate to evolve around z ≤1 , we considered three relevant frameworks of effective cosmological dynamics, i.e., the Λ CDM model, the Chevallier-Polarski-Linder parametrization, and a polynomial approach to dark energy. Finally, cumbersome algebra permits passing from f (z ) to f (R ), and the general outcome of our work is the determination of a viable f (R ) function, which effectively describes the observed Universe dynamics.

de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

NASA Astrophysics Data System (ADS)

Cuzinatto, R. R.; de Morais, E. M.; Medeiros, L. G.; Naldoni de Souza, C.; Pimentel, B. M.

2017-04-01

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) P=P(\\varepsilon) for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor a(t). It is shown that the photon non-null mass does not significantly alter the result a\\propto t1/2 valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass m is extremely small) or in Bopp-Podolsky theory (for which m is extremely large).

Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Felice, Antonio De; Tsujikawa, Shinji, E-mail: antoniod@nu.ac.th, E-mail: shinji@rs.kagu.tus.ac.jp

2012-02-01

In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirmmore » that such models are indeed cosmologically viable.« less

Piecewise silence in discrete cosmological models

NASA Astrophysics Data System (ADS)

Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell

2014-05-01

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon ‘piecewise silence’.

Principle of Spacetime and Black Hole Equivalence

NASA Astrophysics Data System (ADS)

Zhang, Tianxi

2016-06-01

Modelling the universe without relying on a set of hypothetical entities (HEs) to explain observations and overcome problems and difficulties is essential to developing a physical cosmology. The well-known big bang cosmology, widely accepted as the standard model, stands on two fundamentals, which are Einstein’s general relativity (GR) that describes the effect of matter on spacetime and the cosmological principle (CP) of spacetime isotropy and homogeneity. The field equation of GR along with the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric of spacetime derived from CP generates the Friedmann equation (FE) that governs the development and dynamics of the universe. The big bang theory has made impressive successes in explaining the universe, but still has problems and solutions of them rely on an increasing number of HEs such as inflation, dark matter, dark energy, and so on. Recently, the author has developed a new cosmological model called black hole universe, which, instead of making many those hypotheses, only includes a new single postulate (or a new principle) to the cosmology - Principle of Spacetime and Black Hole Equivalence (SBHEP) - to explain all the existing observations of the universe and overcome all the existing problems in conventional cosmologies. This study thoroughly demonstrates how this newly developed black hole universe model, which therefore stands on the three fundamentals (GR, CP, and SBHEP), can fully explain the universe as well as easily conquer the difficulties according to the well-developed physics, thus, neither needing any other hypotheses nor existing any unsolved difficulties. This work was supported by NSF/REU (Grant #: PHY-1263253) at Alabama A & M University.

Large scale magnetic fields from torsion modes and massive photon inflation

NASA Astrophysics Data System (ADS)

Garcia de Andrade, L. C.

2017-10-01

Previously, Barrow and Tsagas (2008 Phys. Rev. D 77 107302) showed that a slower decay of magnetic fields are present in open Friedmann universes, with traditional Maxwell equations. In their paper magnetic fields of the order of B˜ 10-33~G , which are far below the value required to seed galactic dynamos, were obtained. In this paper, galactic dynamo seeds of the order of B˜ 10-23~G are obtained from massive electrodynamics in an Einstein-Cartan-Proca expanding universe of de Sitter type. Slow decay of magnetic fields in photon-torsion coupling in quantum electrodynamics (Garcia de Andrade 2011 Phys. Lett. B 468 28) have been recently shown by the author Garcia de Andrade (2012 Phys. Lett. B 711 143) to also not be able to seed galactic dynamos. Torsion modes are constrained by the field equations. Spacetime torsion is shown to be explicitly responsible for the slow decay of a cosmic magnetic field. In the absence of massive photon torsion coupling the magnetic field decay is of the order B˜ t-\\frac{3{2}} , when torsion turns on B˜ t-1.2 . The pure massive-photon-torsion contribution amplifies the magnetic field by B_torsion˜ t0.1 which characterizes an extremely slow magnetic dynamo action due to purely torsion gravitational effects. Recently Barrow, Tsagas and Yamamoto (2012 Phys. Rev. D 86 023535) have obtained superadiabatic amplification of B-fields in Friedmann open cosmology which lies within {10-20~G} and 10-12~G which falls very comfortably within the limits to seed galactic dynamos. The are other simple solutions where a B-field decays as B˜ a-1 , a relatively weak photon-torsion coupling approximation. These solutions are obtained for de Sitter and Friedmann metrics. Numerical values as displayed in this new version of the paper specifically for GUT phases of inflation with and without massive photons; without photons we obtain the well known value of GR which is B_GUT˜ 1048~G while for the values with massive photons one obtains B_GUT/γ˜ 10-3.5Gauss . At the present time one obtains B_today≤slant{10-21.6~G} and with massive photons one obtains B_today/γ˜ 10-1.8~G , which is unfortunately much stronger than the value obtained by astronomical observations of 10-9~G .

Dissipative universe-inflation with soft singularity

NASA Astrophysics Data System (ADS)

Brevik, Iver; Timoshkin, Alexander V.

We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann-Robertson-Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data, while for the scalar-to-tensor ratio, there are minor deviations.

Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos; Vakili, Babak

2016-01-01

We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor a( t), a scalar field with potential function V(φ ) minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(φ ). Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace under the infinitesimal generator of the desired symmetries. It is shown that by applying the Lie symmetry condition the form of the coupling function and also the scalar field potential function may be explicitly determined so that we are able to solve the Wheeler-DeWitt equation. Finally, we show how we can use the Lie symmetries in order to construct conservation laws and exact solutions for the field equations.

Inflationary universe in terms of a van der Waals viscous fluid

NASA Astrophysics Data System (ADS)

Brevik, I.; Elizalde, E.; Odintsov, S. D.; Timoshkin, A. V.

The inflationary expansion of our early-time universe is considered in terms of the van der Waals equation, as equation of state for the cosmic fluid, where a bulk viscosity contribution is assumed to be present. The corresponding gravitational equations for the energy density in a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker universe are solved, and an analytic expression for the scale factor is obtained. Attention is paid, specifically, to the role of the viscosity term in the accelerated expansion; the values of the slow-roll parameters, the spectral index, and the tensor-to-scalar ratio for the van der Waals model are calculated and compared with the most recent astronomical data from the Planck satellite. By imposing reasonable restrictions on the parameters of the van der Waals equation, in the presence of viscosity, it is shown to be possible for this model to comply quite precisely with the observational data. One can therefore conclude that the inclusion of viscosity in the theory of the inflationary epoch may definitely improve the cosmological models.

Integrability from point symmetries in a family of cosmological Horndeski Lagrangians

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos

2017-07-01

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaître-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.

Cosmology of a Friedmann-Lamaître-Robertson-Walker 3-brane, late-time cosmic acceleration, and the cosmic coincidence.

PubMed

Doolin, Ciaran; Neupane, Ishwaree P

2013-04-05

A late epoch cosmic acceleration may be naturally entangled with cosmic coincidence--the observation that at the onset of acceleration the vacuum energy density fraction nearly coincides with the matter density fraction. In this Letter we show that this is indeed the case with the cosmology of a Friedmann-Lamaître-Robertson-Walker (FLRW) 3-brane in a five-dimensional anti-de Sitter spacetime. We derive the four-dimensional effective action on a FLRW 3-brane, from which we obtain a mass-reduction formula, namely, M(P)(2) = ρ(b)/|Λ(5)|, where M(P) is the effective (normalized) Planck mass, Λ(5) is the five-dimensional cosmological constant, and ρ(b) is the sum of the 3-brane tension V and the matter density ρ. Although the range of variation in ρ(b) is strongly constrained, the big bang nucleosynthesis bound on the time variation of the effective Newton constant G(N) = (8πM(P)(2))(-1) is satisfied when the ratio V/ρ ≳ O(10(2)) on cosmological scales. The same bound leads to an effective equation of state close to -1 at late epochs in accordance with astrophysical and cosmological observations.

Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

NASA Astrophysics Data System (ADS)

Tomassini, Luca; Viaggiu, Stefano

2014-09-01

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realization of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space. In loving memory of Francesco Saverio de Blasi, mathematician and friend.

A unified picture of cosmological entropy on apparent horizon in F(R, G) gravity

NASA Astrophysics Data System (ADS)

Keskin, Ali Ihsan; Acikgoz, Irfan

2017-10-01

In this study, the validity of the generalized second law of thermodynamics (GSLT) has been investigated in F(R, G) gravity. We consider that the boundary of the universe is surrounded by an apparent horizon in the spatially flat Friedmann-Robertson-Walker (FRW) universe, and we take into account the Hawking temperature on the horizons. The unified solutions of the field equations corresponding to gravity theory have been applied to the validity of the GSLT frame, and in this way, both the solutions have been verified and all the expansion history of the universe has been shown in a unified picture.

Superluminality in dilatationally invariant generalized Galileon theories

NASA Astrophysics Data System (ADS)

Kolevatov, R. S.

2015-12-01

We consider small perturbations about homogeneous backgrounds in dilatationally invariant Galileon models. The issues we address are stability (absence of ghosts and gradient instabilities) and superluminality. We show that in the Minkowski background, it is possible to construct the Lagrangian in such a way that any homogeneous Galileon background solution is stable and small perturbations about it are subluminal. On the other hand, in the case of Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds, for any Lagrangian functions there exist homogeneous background solutions to the Galileon equation of motion and time dependence of the scale factor, such that the stability conditions are satisfied, but the Galileon perturbations propagate with superluminal speed.

On gravitational energy in conformal teleparallel gravity

NASA Astrophysics Data System (ADS)

da Silva, J. G.; Ulhoa, S. C.

2017-07-01

The paper deals with the definition of gravitational energy in conformal teleparallel gravity. The total energy is defined by means of the field equations which allow a local conservation law. Then such an expression is analyzed for a homogeneous and isotropic Universe. This model is implemented by the Friedmann-Robertson-Walker (FRW) line element. The energy of the Universe in the absence of matter is identified with the dark energy, however it can be expanded for curved models defining such an energy as the difference between the total energy and the energy of the perfect fluid which is the matter field in the FRW model.

Inhomogeneous cosmology and backreaction: Current status and future prospects

NASA Astrophysics Data System (ADS)

Bolejko, Krzysztof; Korzyński, Mikołaj

Astronomical observations reveal hierarchical structures in the universe, from galaxies, groups of galaxies, clusters and superclusters, to filaments and voids. On the largest scales, it seems that some kind of statistical homogeneity can be observed. As a result, modern cosmological models are based on spatially homogeneous and isotropic solutions of the Einstein equations, and the evolution of the universe is approximated by the Friedmann equations. In parallel to standard homogeneous cosmology, the field of inhomogeneous cosmology and backreaction is being developed. This field investigates whether small scale inhomogeneities via nonlinear effects can backreact and alter the properties of the universe on its largest scales, leading to a non-Friedmannian evolution. This paper presents the current status of inhomogeneous cosmology and backreaction. It also discusses future prospects of the field of inhomogeneous cosmology, which is based on a survey of 50 academics working in the field of inhomogeneous cosmology.

Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields

NASA Astrophysics Data System (ADS)

Asenjo, Felipe A.; Hojman, Sergio A.

2017-07-01

A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.

An introduction to tensor calculus, relativity and cosmology /3rd edition/

NASA Astrophysics Data System (ADS)

Lawden, D. F.

This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

Modified first-order Hořava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in a power-law F(R) model

NASA Astrophysics Data System (ADS)

Carloni, Sante; Chaichian, Masud; Nojiri, Shin'Ichi; Odintsov, Sergei D.; Oksanen, Markku; Tureanu, Anca

2010-09-01

We propose the most general modified first-order Hořava-Lifshitz gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat Friedmann-Robertson-Walker (FRW) space-time, demonstrating many of the features of the general theory. It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent. As a large class of such theories, the modified Hořava-Lifshitz F(R) gravity is introduced. The study of its ultraviolet properties shows that its z=3 version seems to be renormalizable in the same way as the original Hořava-Lifshitz proposal. The Hamiltonian analysis of the modified Hořava-Lifshitz F(R) gravity shows that it is in general a consistent theory. The F(R) gravity action is also studied in the fixed-gauge form, where the appearance of a scalar field is particularly illustrative. Then the spatially-flat FRW cosmology for this F(R) gravity is investigated. It is shown that a special choice of parameters for this theory leads to the same equations of motion as in the case of traditional F(R) gravity. Nevertheless, the cosmological structure of the modified Hořava-Lifshitz F(R) gravity turns out to be much richer than for its traditional counterpart. The emergence of multiple de Sitter solutions indicates the possibility of unification of early-time inflation with late-time acceleration within the same model. Power-law F(R) theories are also investigated in detail. It is analytically shown that they have a quite rich cosmological structure: early-/late-time cosmic acceleration of quintessence, as well as of phantom types. Also it is demonstrated that all the four known types of finite-time future singularities may occur in the power-law Hořava-Lifshitz F(R) gravity. Finally, a covariant proposal for (renormalizable) F(R) gravity within the Hořava-Lifshitz spirit is presented.

A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

NASA Astrophysics Data System (ADS)

Kirchner, U.

2004-08-01

We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann Lemaître Robertson Walker (FLRW) models. We discuss 'vacuum bubbles' and closed open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

Quantum cosmology of a conformal multiverse

NASA Astrophysics Data System (ADS)

Robles-Pérez, Salvador J.

2017-09-01

This paper studies the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, and all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a nonzero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other nonlocal processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a de Sitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (WKB) time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes, and thus, the effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each spacetime of the entangled pair. We find that the largest modes of the scalar field are unaware of the entanglement between the universes, but the effects can be significant for the lowest modes, allowing us to compute, in principle, detailed observational imprints of the multiverse in the properties of a single universe like ours.

Effects of cosmic acceleration on black hole thermodynamics

NASA Astrophysics Data System (ADS)

Mandal, Abhijit

2016-07-01

Direct local impacts of cosmic acceleration upon a black hole are matters of interest. Babichev et. al. had published before that the Friedmann equations which are prevailing the part of fluid filled up in the universe to lead (or to be very specific, `dominate') the other constituents of universe and are forcing the universe to undergo present-day accelerating phase (or to lead to violate the strong energy condition and latter the week energy condition), will themselves tell that the rate of change of mass of the central black hole due to such exotic fluid's accretion will essentially shrink the mass of the black hole. But this is a global impact indeed. The local changes in the space time geometry next to the black hole can be analysed from a modified metric governing the surrounding space time of a black hole. A charged deSitter black hole solution encircled by quintessence field is chosen for this purpose. Different thermodynamic parameters are analysed for different values of quintessence equation of state parameter, ω_q. Specific jumps in the nature of the thermodynamic space near to the quintessence or phantom barrier are noted and physically interpreted as far as possible. Nature of phase transitions and the situations at which these transitions are taking place are also explored. It is determined that before quintessence starts to work (ω_q=-0.33>-1/3) it was preferable to have a small unstable black hole followed by a large stable one. But in quintessence (-1/3>ω_q>-1), black holes are destined to be unstable large ones pre-quelled by stable/ unstable small/ intermediate mass black holes.

Confinement and hadron-hadron interactions by general relativistic methods

NASA Astrophysics Data System (ADS)

Recami, Erasmo

By postulating covariance of physical laws under global dilations, one can describe gravitational and strong interactions in a unified way. Namely, in terms of the new discrete dilational degree of freedom, our cosmos and hadrons can be regarded as finite, similar systems. And a discrete hierarchy of finite ``universes'' may be defined, which are governed by fields with strengths inversally proportional to their radii; in each universe an Equivalence Principle holds, so that the relevant field can be there geometrized. Scaled-down Einstein equations -with cosmological term- are assumed to hold inside hadrons (= strong micro-cosmoses); and they yield in a natural way classical confinement, as well as ``asymptotic freedom'', of the hadron constituents. In other words, the association of strong micro-universes of Friedmann type with hadrons (i.e., applying the methods of General Relativity to subnuclear particle physics) allows avoiding recourse to phenomenological models such as the Bag Model. Inside hadrons we have to deal with a tensorial field (= strong gravity), and hadron constituents are supposed to exchange spin-2 ``gluons''. Our approach allows us also to write down a tensorial, bi-scale field theory of hadron-hadron interactions, based on modified Einstein-type equations here proposed for strong interactions in our space. We obtain in particular: (i) the correct Yukawa behaviour of the strong scalar potential at the static limit and for r>~l fm; (ii) the value of hadron radii. As a byproduct, we derive a whole ``numerology'', connecting our gravitational cosmos with the strong micro-cosmoses (hadrons), such that it does imply no variation of G with the epoch. Finally, since a structute of the ``micro-universe'' type seems to be characteristic even of leptons, a hope for the future is including also weak interactions in our classical unification of the fundamental forces.

The quantum realm of the ''Little Sibling'' of the Big Rip singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albarran, Imanol; Bouhmadi-López, Mariam; Cabral, Francisco

We analyse the quantum behaviour of the ''Little Sibling'' of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler-DeWitt (WDW) equation. The classical model is based on a Friedmann-Lemaître-Robertson-Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve themore » WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace-Beltrami factor-ordering, using a Born-Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.« less

Self-similar motion of a Nambu-Goto string

NASA Astrophysics Data System (ADS)

Igata, Takahisa; Houri, Tsuyoshi; Harada, Tomohiro

2016-09-01

We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo)Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lemaître-Robertson-Walker expanding universe with self-similarity and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of the cosmic expansion and string tension. We also show the instability for linear radial perturbation of the circular solutions.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-05-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w = 0) at late times. The equation of state smoothly transitions from the early to late-time behavior and exactly describes the evolution of a species with a Dirac Delta function distribution in momentum magnitudes |p_0| (i.e. all particles have the same |p_0|). Such a component, here termed "hot matter", is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of super-horizon perturbations in each case. The idealized model recovers t(a) to better than 1.5% accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-07-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w= 0) at late times. The equation of state smoothly transitions from the early- to late-time behaviour and exactly describes the evolution of a species with a Dirac delta function distribution in momentum magnitudes |{p}_0| (i.e. all particles have the same |{p}_0|). Such a component, here termed `hot matter', is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of superhorizon perturbations in each case. The idealized model recovers t(a) to better than 1.5 per cent accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Tsallis holographic dark energy

NASA Astrophysics Data System (ADS)

Tavayef, M.; Sheykhi, A.; Bamba, Kazuharu; Moradpour, H.

2018-06-01

Employing the modified entropy-area relation suggested by Tsallis and Cirto [1], and the holographic hypothesis, a new holographic dark energy (HDE) model is proposed. Considering a flat Friedmann-Robertson-Walker (FRW) universe in which there is no interaction between the cosmos sectors, the cosmic implications of the proposed HDE are investigated. Interestingly enough, we find that the identification of IR-cutoff with the Hubble radius, can lead to the late time accelerated Universe even in the absence of interaction between two dark sectors of the Universe. This is in contrast to the standard HDE model with Hubble cutoff, which does not imply the accelerated expansion, unless the interaction is taken into account.

Palatini formulation of f( R, T) gravity theory, and its cosmological implications

NASA Astrophysics Data System (ADS)

Wu, Jimin; Li, Guangjie; Harko, Tiberiu; Liang, Shi-Dong

2018-05-01

We consider the Palatini formulation of f( R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f( R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type f=R-α ^2/R+g(T) and f=R+α ^2R^2+g(T) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.

Model-independent reconstruction of f( T) teleparallel cosmology

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

2017-11-01

We propose a model-independent formalism to numerically solve the modified Friedmann equations in the framework of f( T) teleparallel cosmology. Our strategy is to expand the Hubble parameter around the redshift z=0 up to a given order and to adopt cosmographic bounds as initial settings to determine the corresponding f(z)≡ f(T(H(z))) function. In this perspective, we distinguish two cases: the first expansion is up to the jerk parameter, the second expansion is up to the snap parameter. We show that inside the observed redshift domain z≤ 1, only the net strength of f( z) is modified passing from jerk to snap, whereas its functional behavior and shape turn out to be identical. As first step, we set the cosmographic parameters by means of the most recent observations. Afterwards, we calibrate our numerical solutions with the concordance Λ CDM model. In both cases, there is a good agreement with the cosmological standard model around z≤ 1, with severe discrepancies outer of this limit. We demonstrate that the effective dark energy term evolves following the test-function: f(z)=A+B{z}^2e^{Cz}. Bounds over the set A, B, C are also fixed by statistical considerations, comparing discrepancies between f( z) with data. The approach opens the possibility to get a wide class of test-functions able to frame the dynamics of f( T) without postulating any model a priori. We thus re-obtain the f( T) function through a back-scattering procedure once f( z) is known. We figure out the properties of our f( T) function at the level of background cosmology, to check the goodness of our numerical results. Finally, a comparison with previous cosmographic approaches is carried out giving results compatible with theoretical expectations.

Effects of sterile neutrino and extra-dimension on big bang nucleosynthesis

NASA Astrophysics Data System (ADS)

Jang, Dukjae; Kusakabe, Motohiko; Cheoun, Myung-Ki

2018-04-01

We study effects of the sterile neutrino in the five-dimensional universe on the big bang nucleosynthesis (BBN). Since the five-dimensional universe model leads to an additional term in the Friedmann equation and the energy density of the sterile neutrino increases the total energy density, this model can affect the primordial abundance via changing the cosmic expansion rate. The energy density of the sterile neutrino can be determined by a rate equation for production of the sterile neutrino. We show that not only the mixing angle and the mass of the sterile neutrino, but also a resonant effect in the oscillation between sterile and active neutrinos is important to determine a relic abundance of the sterile neutrino. In this study, we also investigate how the sterile neutrino in extra-dimensional model can affect the BBN, and constrain the parameters related to the above properties of the sterile neutrino by using the observational primordial abundances of light elements.

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.

2009-12-15

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), andmore » (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.« less

Classical and quantum cosmology of minimal massive bigravity

NASA Astrophysics Data System (ADS)

Darabi, F.; Mousavi, M.

2016-10-01

In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.

Third Quantization and Quantum Universes

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

2014-01-01

We study the third quantization of the Friedmann-Robertson-Walker cosmology with N-minimal massless fields. The third quantized Hamiltonian for the Wheeler-DeWitt equation in the minisuperspace consists of infinite number of intrinsic time-dependent, decoupled oscillators. The Hamiltonian has a pair of invariant operators for each universe with conserved momenta of the fields that play a role of the annihilation and the creation operators and that construct various quantum states for the universe. The closed universe exhibits an interesting feature of transitions from stable states to tachyonic states depending on the conserved momenta of the fields. In the classical forbidden unstable regime, the quantum states have googolplex growing position and conjugate momentum dispersions, which defy any measurements of the position of the universe.

Nonminimal kinetic coupled gravity: Inflation on the warped DGP brane

NASA Astrophysics Data System (ADS)

Darabi, F.; Parsiya, A.; Atazadeh, K.

2016-03-01

We consider the nonminimally kinetic coupled version of DGP brane model, where the kinetic term of the scalar field is coupled to the metric and Einstein tensor on the brane by a coupling constant ζ. We obtain the corresponding field equations, using the Friedmann-Robertson-Walker metric and the perfect fluid, and study the inflationary scenario to confront the numerical analysis of six typical scalar field potentials with the current observational results. We find that among the suggested potentials and coupling constants, subject to the e-folding N = 60, the potentials V (ϕ) = σϕ, V (ϕ) = σϕ2 and V (ϕ) = σϕ3 provide the best fits with both Planck+WP+highL data and Planck+WP+highL+BICEP2 data.

Mathematical issues in eternal inflation

NASA Astrophysics Data System (ADS)

Singh Kohli, Ikjyot; Haslam, Michael C.

2015-04-01

In this paper, we consider the problem of the existence and uniqueness of solutions to the Einstein field equations for a spatially flat Friedmann-Lemaître-Robertson-Walker universe in the context of stochastic eternal inflation, where the stochastic mechanism is modelled by adding a stochastic forcing term representing Gaussian white noise to the Klein-Gordon equation. We show that under these considerations, the Klein-Gordon equation actually becomes a stochastic differential equation. Therefore, the existence and uniqueness of solutions to Einstein’s equations depend on whether the coefficients of this stochastic differential equation obey Lipschitz continuity conditions. We show that for any choice of V(φ ), the Einstein field equations are not globally well-posed, hence, any solution found to these equations is not guaranteed to be unique. Instead, the coefficients are at best locally Lipschitz continuous in the physical state space of the dynamical variables, which only exist up to a finite explosion time. We further perform Feller’s explosion test for an arbitrary power-law inflaton potential and prove that all solutions to the Einstein field equations explode in a finite time with probability one. This implies that the mechanism of stochastic inflation thus considered cannot be described to be eternal, since the very concept of eternal inflation implies that the process continues indefinitely. We therefore argue that stochastic inflation based on a stochastic forcing term would not produce an infinite number of universes in some multiverse ensemble. In general, since the Einstein field equations in both situations are not well-posed, we further conclude that the existence of a multiverse via the stochastic eternal inflation mechanism considered in this paper is still very much an open question that will require much deeper investigation.

Evading the non-continuity equation in the f( R, T) cosmology

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Correa, R. A. C.; Ribeiro, G.

2018-03-01

We present a new approach for the f( R, T) gravity formalism, by thoroughly exploring the extra terms of its effective energy-momentum tensor T_{μ ν }^eff, which we name \\tilde{T}_{μ ν }, so that T_{μ ν }^eff=T_{μ ν }+\\tilde{T}_{μ ν }, with T_{μ ν } being the usual energy-momentum tensor of matter. Purely from the Bianchi identities, we obtain the conservation of both parts of the effective energy-momentum tensor, rather than the non-conservation of T_{μ ν }, originally occurring in the f( R, T) theories. In this way, the intriguing scenario of matter creation, which still lacks observational evidence, is evaded. One is left, then, with two sets of cosmological equations to be solved: the Friedmann-like equations along with the conservation of T_{μ ν } and along with the conservation of \\tilde{T}_{μ ν }. We present a physical interpretation for the conservation of \\tilde{T}_{μ ν }, which can be related to the presence of stiff matter in the universe. The cosmological consequences of this approach are presented and discussed as well as the benefits of evading the matter energy-momentum tensor non-conservation.

A study of perturbations in scalar-tensor theory using 1 + 3 covariant approach

NASA Astrophysics Data System (ADS)

Ntahompagaze, Joseph; Abebe, Amare; Mbonye, Manasse

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke sub-class, and one that also takes note of the latter’s equivalence with f(R) gravitation theories. A 1 + 3 covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaître-Robertson-Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for Rn models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy-density perturbations is oscillatory, with growing amplitudes for n > 1, and with decaying amplitudes for 0 < n < 1. This is a new result.

The Problem of Inertia in a Friedmann Universe

NASA Technical Reports Server (NTRS)

Kazanas, Demosthenes

2012-01-01

In this talk I will discuss the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass $m$ by integrating over the contributions from all the matter in the universe. The resulting inertial force has the form $F = -kma$ where the constant $k < 1 $ depends on the choice of the cosmological parameters such as $\\Omega_{M},\\ \\Omega_{\\Lambda}, $ and $\\Omega_{R}$. The values of $k$ obtained suggest that inertial contribution from dark matter can be the source for the missing part of the inertial force.

Does iron inhibit cryptoendolithic microbial communities?

NASA Technical Reports Server (NTRS)

Johnston, C. G.; Vestal, J. R.; Friedmann, E. I. (Principal Investigator)

1988-01-01

Photosynthetic activity of three cryptoendolithic microbial communities was studied under controlled conditions in the laboratory. In two of these communities, the dominant organisms were lichens, collected from Linnaeus Terrace and from Battleship Promontory. The third community, dominated by cyanobacteria, was collected from Battleship Promontory. Both sites are in the ice-free valleys of southern Victoria Land. Previous efforts have shown how physical conditions can influence metabolic activity in endolithic communities (Kappen and Friedmann 1983; Kappen, Friedmann, and Garty 1981; Vestal, Federle, and Friedmann 1984). Biological activity can also be strongly influenced by the chemical environment. Inorganic nutrients such as nitrate, ammonia, and phosphate are often limiting factors, so their effects on photosynthetic carbon-14 bicarbonate incorporation were investigated. Iron and manganese are two metals present in Linnaeus Terrace and Battleship Promontory sandstones, and their effects on photosynthesis were also studied. The results may add to our understanding of biogeochemical interactions within this unique microbial community.

Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaître-Robertson-Walker spacetimes: Stability and isoperimetric inequalities

NASA Astrophysics Data System (ADS)

Mach, Patryk; Xie, Naqing

2017-10-01

We investigate toroidal marginally outer trapped surfaces (MOTS) and marginally outer trapped tubes (MOTT) in closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. They are constructed by embedding constant mean curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.

Bianchi class B spacetimes with electromagnetic fields

NASA Astrophysics Data System (ADS)

Yamamoto, Kei

2012-02-01

We carry out a thorough analysis on a class of cosmological space-times which admit three spacelike Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of electro-vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those analyses, we discuss the relation between those homogeneous models and perturbations of open Friedmann-Lemaitre-Robertson-Walker universes. We argue that the electro-vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations.

Holographic dark energy in braneworld models with moving branes and the w = -1 crossing

NASA Astrophysics Data System (ADS)

Saridakis, E. N.

2008-04-01

We apply the bulk holographic dark energy in general 5D two-brane models. We extract the Friedmann equation on the physical brane and we show that in the general moving-brane case the effective 4D holographic dark energy behaves as a quintom for a large parameter-space area of a simple solution subclass. We find that wΛ was larger than -1 in the past while its present value is wΛ0≈-1.05, and the phantom bound wΛ = -1 was crossed at zp≈0.41, a result in agreement with observations. Such a behavior arises naturally, without the inclusion of special fields or potential terms, but a fine-tuning between the 4D Planck mass and the brane tension has to be imposed.

Tensor perturbations during inflation in a spatially closed Universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonga, Béatrice; Gupt, Brajesh; Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu

2017-05-01

In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited tomore » the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.« less

Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

NASA Astrophysics Data System (ADS)

Seriu, Masafumi

2015-10-01

We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.

Perturbation theory for cosmologies with nonlinear structure

NASA Astrophysics Data System (ADS)

Goldberg, Sophia R.; Gallagher, Christopher S.; Clifton, Timothy

2017-11-01

The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for nonlinear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. This uses both post-Newtonian gravity and cosmological perturbation theory, and can be used to model realistic cosmological scenarios including matter, radiation and a cosmological constant. We find that the resulting field equations can be written as a hierarchical set of perturbation equations. At leading-order, these equations allow us to recover a standard set of Friedmann equations, as well as a Newton-Poisson equation for the inhomogeneous part of the Newtonian energy density in an expanding background. For the perturbations in the large-scale cosmology, however, we find that the field equations are sourced by both nonlinear and mode-mixing terms, due to the existence of small-scale structures. These extra terms should be expected to give rise to new gravitational effects, through the mixing of gravitational modes on small and large scales—effects that are beyond the scope of standard linear cosmological perturbation theory. We expect our formalism to be useful for accurately modeling gravitational physics in universes that contain nonlinear structures, and for investigating the effects of nonlinear gravity in the era of ultra-large-scale surveys.

Multifluid cosmology: An illustration of fundamental principles

NASA Astrophysics Data System (ADS)

Comer, G. L.; Peter, Patrick; Andersson, N.

2012-05-01

Our current understanding of the Universe depends on the interplay of several distinct matter components, which interact mainly through gravity, and electromagnetic radiation. The nature of the different components, and possible interactions, tends to be based on the notion of coupled perfect fluids (or scalar fields). This approach is somewhat naive, especially if one wants to be able to consider issues involving heat flow, dissipative mechanisms, or Bose-Einstein condensation of dark matter. We argue that a more natural starting point would be the multipurpose variational relativistic multifluid system that has so far mainly been applied to neutron star astrophysics. As an illustration of the fundamental principles involved, we develop the formalism for determining the nonlinear cosmological solutions to the Einstein equations for a general relativistic two-fluid model for a coupled system of matter (nonzero rest mass) and radiation (zero rest mass). The two fluids are allowed to interpenetrate and exhibit a relative flow with respect to each other, implying, in general, an anisotropic Universe. We use initial conditions such that the massless fluid flux dominates early on so that the situation is effectively that of a single-fluid and one has the usual Friedmann-Lemaître-Robertson-Walker spacetime. We find that there is a Bianchi I transition epoch out of which the matter flux dominates. The situation is then effectively that of a single fluid and the spacetime evolves towards the Friedmann-Lemaître-Robertson-Walker form. Such a transition opens up the possibility of imprinting observable consequences at the specific scale corresponding to the transition time.

Astronomical bounds on a cosmological model allowing a general interaction in the dark sector

NASA Astrophysics Data System (ADS)

Pan, Supriya; Mukherjee, Ankan; Banerjee, Narayan

2018-06-01

Non-gravitational interaction between two barotropic dark fluids, namely the pressureless dust and the dark energy in a spatially flat Friedmann-Lemaître-Robertson-Walker model, has been discussed. It is shown that for the interactions that are linear in terms the energy densities of the dark components and their first order derivatives, the net energy density is governed by a second-order differential equation with constant coefficients. Taking a generalized interaction, which includes a number of already known interactions as special cases, the dynamics of the universe is described for three types of the dark energy equation of state, namely that of interacting quintessence, interacting vacuum energy density, and interacting phantom. The models have been constrained using the standard cosmological probes, Supernovae Type Ia data from joint light curve analysis and the observational Hubble parameter data. Two geometric tests, the cosmographic studies, and the Om diagnostic have been invoked so as to ascertain the behaviour of the present model vis-a-vis the Λ-cold dark matter model. We further discussed the interacting scenarios taking into account the thermodynamic considerations.

Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy

NASA Astrophysics Data System (ADS)

Komatsu, Nobuyoshi

2017-11-01

A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the α th power of the Hubble parameter, where α is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constantlike when α is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

Ghost Dark Energy with Sign-changeable Interaction Term

NASA Astrophysics Data System (ADS)

Zadeh, M. Abdollahi; Sheykhi, A.; Moradpour, H.

2017-11-01

Regarding the Veneziano ghost of QCD and its generalized form, we consider a Friedmann-Robertson-Walker (FRW) universe filled by a pressureless matter and a dark energy component interacting with each other through a mutual sign-changeable interaction of positive coupling constant. Our study shows that, at the late time, for the deceleration parameter we have q → -1, while the equation of state parameter of the interacting ghost dark energy (GDE) does not cross the phantom line, namely ω D ≥ -1. We also extend our study to the generalized ghost dark energy (GGDE) model and show that, at late time, the equation of state parameter of the interacting GGDE also respects the phantom line in both flat and non-flat universes. Moreover, we find out that, unlike the non-flat universe, we have q → -1 at late time for flat FRW universe. In order to make the behavior of the underlying models more clear, the deceleration parameter q as well as the equation of state parameter w D for flat and closed universes have been plotted against the redshift parameter, z. All of the studied cases admit a transition in the expansion history of universe from a deceleration phase to an accelerated one around z ≈ 0.6.

Preliminary report on radiocarbon dating of cryptoendolithic microorganisms

NASA Technical Reports Server (NTRS)

Bonani, G.; Friedmann, E. I.; Ocampo-Friedmann, R.; McKay, C. P.; Woelfli, W.

1988-01-01

The existence of microbial communities living inside desert rocks has been reported by FRIEDMANN et al. (1967, 1976), first in rocks collected from the hot and dry Negev desert and later in rocks in the frigid Ross Desert of Southern Victoria Land, Antarctica. The extremely inhospitable climatic conditions in both places has led to the suggestion that these organisms have very low rates of metabolism and may, in addition, be very old (FRIEDMANN 1982). Our preliminary measurements showed a 14C deficiency indicating a carbon age in the order of magnitude of 10(3) years.

Tunneling in quantum cosmology and holographic SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Nakano, Yoshimasa; Tachibana, Motoi; Toyoda, Fumihiko

2018-03-01

We study the time evolution of the early Universe, which is developed by a cosmological constant Λ4 and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker space-time. The renormalized vacuum expectation value of the energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as C . The evolution is controlled by this radiation C and the cosmological constant Λ4. For positive Λ4, an inflationary solution is obtained at late time. When C is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.

The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomes, Adalto R.; Amendola, Luca, E-mail: argomes.ufma@gmail.com, E-mail: l.amendola@thphys.uni-heidelberg.de

We consider the general scalar field Horndeski Lagrangian coupled to dark matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of dark matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problemmore » since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.« less

Modified equations, rational solutions, and the Painleve property for the Kadomtsev--Petviashvili and Hirota--Satsuma equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weiss, J.

1985-09-01

We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painleve property, a Baecklund transformation is defined in terms of an expansion about the singular manifold. This Baecklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Baecklund transformations of the modified equations provides a method for themore » iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev--Petviashvili equation and the Hirota--Satsuma equations.« less

Using Mathematical Algorithms to Modify Glomerular Filtration Rate Estimation Equations

PubMed Central

Zhu, Bei; Wu, Jianqing; Zhu, Jin; Zhao, Weihong

2013-01-01

Background The equations provide a rapid and low-cost method of evaluating glomerular filtration rate (GFR). Previous studies indicated that the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease-Epidemiology (CKD-EPI) and MacIsaac equations need further modification for application in Chinese population. Thus, this study was designed to modify the three equations, and compare the diagnostic accuracy of the equations modified before and after. Methodology With the use of 99 mTc-DTPA renal dynamic imaging as the reference GFR (rGFR), the MDRD, CKD-EPI and MacIsaac equations were modified by two mathematical algorithms: the hill-climbing and the simulated-annealing algorithms. Results A total of 703 Chinese subjects were recruited, with the average rGFR 77.14±25.93 ml/min. The entire modification process was based on a random sample of 80% of subjects in each GFR level as a training sample set, the rest of 20% of subjects as a validation sample set. After modification, the three equations performed significant improvement in slop, intercept, correlated coefficient, root mean square error (RMSE), total deviation index (TDI), and the proportion of estimated GFR (eGFR) within 10% and 30% deviation of rGFR (P10 and P30). Of the three modified equations, the modified CKD-EPI equation showed the best accuracy. Conclusions Mathematical algorithms could be a considerable tool to modify the GFR equations. Accuracy of all the three modified equations was significantly improved in which the modified CKD-EPI equation could be the optimal one. PMID:23472113

A new modified CKD-EPI equation for Chinese patients with type 2 diabetes.

PubMed

Liu, Xun; Gan, Xiaoliang; Chen, Jinxia; Lv, Linsheng; Li, Ming; Lou, Tanqi

2014-01-01

To improve the performance of glomerular filtration rate (GFR) estimating equation in Chinese type 2 diabetic patients by modification of the CKD-EPI equation. A total of 1196 subjects were enrolled. Measured GFR was calibrated to the dual plasma sample 99mTc-DTPA-GFR. GFRs estimated by the re-expressed 4-variable MDRD equation, the CKD-EPI equation and the Asian modified CKD-EPI equation were compared in 351 diabetic/non-diabetic pairs. And a new modified CKD-EPI equation was reconstructed in a total of 589 type 2 diabetic patients. In terms of both precision and accuracy, GFR estimating equations all achieved better results in the non-diabetic cohort comparing with those in the type 2 diabetic cohort (30% accuracy, P≤0.01 for all comparisons). In the validation data set, the new modified equation showed less bias (median difference, 2.3 ml/min/1.73 m2 for the new modified equation vs. ranged from -3.8 to -7.9 ml/min/1.73 m2 for the other 3 equations [P<0.001 for all comparisons]), as was precision (IQR of the difference, 24.5 ml/min/1.73 m2 vs. ranged from 27.3 to 30.7 ml/min/1.73 m2), leading to a greater accuracy (30% accuracy, 71.4% vs. 55.2% for the re-expressed 4 variable MDRD equation and 61.0% for the Asian modified CKD-EPI equation [P = 0.001 and P = 0.02]). A new modified CKD-EPI equation for type 2 diabetic patients was developed and validated. The new modified equation improves the performance of GFR estimation.

Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models

NASA Astrophysics Data System (ADS)

Nojiri, Shin'Ichi; Odintsov, Sergei D.

2011-08-01

The classical generalization of general relativity is considered as the gravitational alternative for a unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of a number of modified theories, including traditional F(R) and Hořava-Lifshitz F(R) gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, non-minimally coupled models, and power-counting renormalizable covariant gravity are discussed. Different representations of and relations between such theories are investigated. It is shown that some versions of the above theories may be consistent with local tests and may provide a qualitatively reasonable unified description of inflation with the dark energy epoch. The cosmological reconstruction of different modified gravities is provided in great detail. It is demonstrated that eventually any given universe evolution may be reconstructed for the theories under consideration, and the explicit reconstruction is applied to an accelerating spatially flat Friedmann-Robertson-Walker (FRW) universe. Special attention is paid to Lagrange multiplier constrained and conventional F(R) gravities, for latter F(R) theory, the effective ΛCDM era and phantom divide crossing acceleration are obtained. The occurrences of the Big Rip and other finite-time future singularities in modified gravity are reviewed along with their solutions via the addition of higher-derivative gravitational invariants.

Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation

NASA Astrophysics Data System (ADS)

Gegenhasi; Li, Ya-Qian; Zhang, Duo-Duo

2018-04-01

In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources. Supported by the National Natural Science Foundation of China under Grant Nos. 11601247 and 11605096, the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant Nos. 2016MS0115 and 2015MS0116 and the Innovation Fund Programme of Inner Mongolia University No. 20161115

Probing dark energy with braneworld cosmology in the light of recent cosmological data

NASA Astrophysics Data System (ADS)

García-Aspeitia, Miguel A.; Magaña, Juan; Hernández-Almada, A.; Motta, V.

We investigate a brane model based on Randall-Sundrum scenarios with a generic dark energy component. The latter drives the accelerated expansion at late-times of the universe. In this scheme, extra terms are added into Einstein Field equations that are propagated to the Friedmann equations. To constrain the dark energy equation-of-state (EoS) and the brane tension we use observational data with different energy levels (Supernovae Type Ia, H(z), baryon acoustic oscillations, and cosmic microwave background radiation distance, and a joint analysis) in a background cosmology. Beside EoS being consistent with a cosmological constant at the 3σ confidence level for each dataset, the baryon acoustic oscillations probe favors an EoS consistent with a quintessence dark energy. Although we found different lower limit bounds on the brane tension for each dataset, being the most restricted for CMB, there is not enough evidence of modifications in the cosmological evolution of the universe by the existence of an extra dimension within observational uncertainties. Nevertheless, these new bounds are complementary to those obtained by other probes like table-top experiments, Big Bang Nucleosynthesis, and stellar dynamics. Our results show that a further test of the braneworld model with appropriate correction terms or a profound analysis with perturbations, may be needed to improve the constraints provided by the current data.

Thermodynamics and cosmological reconstruction in f(T , B) gravity

NASA Astrophysics Data System (ADS)

Bahamonde, Sebastian; Zubair, M.; Abbas, G.

2018-03-01

Recently, it was formulated a teleparallel theory called f(T , B) gravity which connects both f(T) and f(R) under suitable limits. In this theory, the function in the action is assumed to depend on the torsion scalar T and also on a boundary term related with the divergence of torsion, B = 2∇μTμ. In this work, we study different features of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation TˆhSeff = - dE + WdV, where Tˆh is the horizon temperature and Seff is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium. We also formulate the constraint for the validity of the generalised second law of thermodynamics (GSLT). Additionally, using a cosmological reconstruction technique, we show that both f(T , B) and - T + F(B) gravity can mimic power-law, de-Sitter and ΛCDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions.

Exotic singularities and spatially curved loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Parampreet; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5; Vidotto, Francesca

2011-03-15

We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of k={+-}1 Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the nontrivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities, are ignored by quantum gravity when spatial curvature is negative, as was previouslymore » found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with nonzero spatial curvature.« less

Statistical description of massless excitations within a sphere with a linear equation of state and the dark energy case

NASA Astrophysics Data System (ADS)

Viaggiu, S.

2018-04-01

In this paper, we continue the investigations present in Refs. 1-3. In particular, we extend the theorem proved in Ref. 3 to any massless excitation in a given spherical box. As a first interesting result, we show that it is possible, contrary to the black hole case studied in detail in Refs. 1-3, to build macroscopic configurations with a dark energy equation of state. To this purpose, by requiring a stable configuration, a macroscopic dark fluid is obtained with an internal energy U scaling as the volume V, but with a fundamental correction looking like ˜ 1/R motivated by quantum fluctuations. Thanks to the proposition in Sec. 3 (and in Ref. 3 for gravitons), one can depict the dark energy in terms of massless excitations with a discrete spectrum. This fact opens the possibility to test a possible physical mechanism converting usual radiation into dark energy in a macroscopic configuration, also in a cosmological context. In fact, for example, in a Friedmann flat universe with a cosmological constant, particles are marginally trapped at the Hubble horizon for any given comoving observer.

Cosmologies with varying speed of light: kinematic tests

NASA Astrophysics Data System (ADS)

Câmara, C. S.; Carvalho, J. C.; de Garcia Maia, M. R.

2003-08-01

In the last few years, there have appeared in the literature several models with variation of the fundamental constants of Nature, such as the speed of light (c), the elementary electric charge (e) and the Planck constant (h). The two main motivations for such interest are: (i) observations related to quasars that seem to indicate the fine structure constant is changing with time and (ii) the possibility that these models may solve some long standing problems of the standard cosmological model, without the need for inflation. In the present work, we obtain the expressions for lookback time, age of the universe, luminosity distance, angular diameter, and galaxy number counts versus redshift for the cosmological models with a power law dependence of the speed of light on the scale factor and the Hubble parameter. The Lorentz invariance and the principle of the general covariance are violated and the gravitational field equations have the same form as Einstein field equations with cosmological constant in a preferred reference frame postulated by the theory. We analyse the closed, open and flat Friedmann-Robertson-Walker (FRW) geometries. We have also obtained the limits imposed by the kinematic tests for the exponents m and n of the power laws of these models.

Exact geodesic distances in FLRW spacetimes

NASA Astrophysics Data System (ADS)

Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

2017-11-01

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

General Second-Order Scalar-Tensor Theory and Self-Tuning

NASA Astrophysics Data System (ADS)

Charmousis, Christos; Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.

2012-02-01

Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lemaître-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.

Unitary evolution of the quantum Universe with a Brown-Kuchař dust

NASA Astrophysics Data System (ADS)

Maeda, Hideki

2015-12-01

We study the time evolution of a wave function for the spatially flat Friedmann-Lemaître-Robertson-Walker Universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchař dust as a matter field in order to introduce a ‘clock’ in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the Universe obeys the classical-time evolution in the late time but its variance diverges.

Horava-Lifshitz cosmology, entropic interpretation and quark-hadron phase transition

NASA Astrophysics Data System (ADS)

Kheyri, F.; Khodadi, M.; Sepangi, Hamid Reza

2013-05-01

Based on the assumptions of the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electroweak transition has occurred at approximately 10 μs after the Big Bang to convert a plasma of free quarks and gluons into hadrons. We consider such a phase transition in the context of a deformed Horava-Lifshitz cosmology. The Friedmann equation for the deformed Horava-Lifshitz universe is obtained using the entropic interpretation of gravity, proposed by Verlinde. We investigate the effects of the parameter ω appearing in the theory on the evolution of the physical quantities relevant to a description of the early universe, namely, the energy density and temperature before, during and after the phase transition. Finally, we study the cross-over phase transition in both high and low temperature regions in view of the recent lattice QCD simulations data.

Generalized ghost pilgrim dark energy in F(T,TG) cosmology

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

2016-07-01

This paper is devoted to study the generalized ghost pilgrim dark energy (PDE) model in F(T,TG) gravity with flat Friedmann-Robertson-Walker (FRW) universe. In this scenario, we reconstruct F(T,TG) models and evaluate the corresponding equation of state (EoS) parameter for different choices of the scale factors. We assume power-law scale factor, scale factor for unification of two phases, intermediate and bouncing scale factor. We study the behavior of reconstructed models and EoS parameters graphically. It is found that all the reconstructed models show decreasing behavior for PDE parameter u = -2. On the other hand, the EoS parameter indicates transition from dust-like matter to phantom era for all choices of the scale factor except intermediate for which this is less than - 1. We conclude that all the results are in agreement with PDE phenomenon.

Latest astronomical constraints on some non-linear parametric dark energy models

NASA Astrophysics Data System (ADS)

Yang, Weiqiang; Pan, Supriya; Paliathanasis, Andronikos

2018-04-01

We consider non-linear redshift-dependent equation of state parameters as dark energy models in a spatially flat Friedmann-Lemaître-Robertson-Walker universe. To depict the expansion history of the universe in such cosmological scenarios, we take into account the large-scale behaviour of such parametric models and fit them using a set of latest observational data with distinct origin that includes cosmic microwave background radiation, Supernove Type Ia, baryon acoustic oscillations, redshift space distortion, weak gravitational lensing, Hubble parameter measurements from cosmic chronometers, and finally the local Hubble constant from Hubble space telescope. The fitting technique avails the publicly available code Cosmological Monte Carlo (COSMOMC), to extract the cosmological information out of these parametric dark energy models. From our analysis, it follows that those models could describe the late time accelerating phase of the universe, while they are distinguished from the Λ-cosmology.

Departures from the Friedmann-Lemaitre-Robertston-Walker Cosmological Model in an Inhomogeneous Universe: A Numerical Examination.

PubMed

Giblin, John T; Mertens, James B; Starkman, Glenn D

2016-06-24

While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, nonlinear, and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaître-Robertson-Walker (FLRW) behavior; however, this universe also exhibits locally inhomogeneous expansion beyond that expected in linear perturbation theory around a FLRW background.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanderveld, R. Ali; Flanagan, Eanna E.; Wasserman, Ira

Recently, there have been suggestions that the Type Ia supernova data can be explained using only general relativity and cold dark matter with no dark energy. In 'Swiss cheese' models of the Universe, the standard Friedmann-Robertson-Walker picture is modified by the introduction of mass-compensating spherical inhomogeneities, typically described by the Lemaitre-Tolman-Bondi metric. If these inhomogeneities correspond to underdense cores surrounded by mass-compensating overdense shells, then they can modify the luminosity distance-redshift relation in a way that can mimic accelerated expansion. It has been argued that this effect could be large enough to explain the supernova data without introducing dark energymore » or modified gravity. We show that the large apparent acceleration seen in some models can be explained in terms of standard weak field gravitational lensing together with insufficient randomization of void locations. The underdense regions focus the light less than the homogeneous background, thus dimming supernovae in a way that can mimic the effects of acceleration. With insufficient randomization of the spatial location of the voids and of the lines of sight, coherent defocusing can lead to anomalously large demagnification effects. We show that a proper randomization of the voids and lines of sight reduces the effect to the point that it can no longer explain the supernova data.« less

Post-Newtonian celestial dynamics in cosmology: Field equations

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.; Petrov, Alexander N.

2013-02-01

Post-Newtonian celestial dynamics is a relativistic theory of motion of massive bodies and test particles under the influence of relatively weak gravitational forces. The standard approach for development of this theory relies upon the key concept of the isolated astronomical system supplemented by the assumption that the background spacetime is flat. The standard post-Newtonian theory of motion was instrumental in the explanation of the existing experimental data on binary pulsars, satellite, and lunar laser ranging, and in building precise ephemerides of planets in the Solar System. Recent studies of the formation of large-scale structures in our Universe indicate that the standard post-Newtonian mechanics fails to describe more subtle dynamical effects in motion of the bodies comprising the astronomical systems of larger size—galaxies and clusters of galaxies—where the Riemann curvature of the expanding Friedmann-Lemaître-Robertson-Walker universe interacts with the local gravitational field of the astronomical system and, as such, cannot be ignored. The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding Universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated astronomical N-body system (the Solar System, a binary star, a galaxy, and a cluster of galaxies). We postulate that the geometric properties of the background manifold are described by a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric governed by two primary components—the dark matter and the dark energy. The dark matter is treated as an ideal fluid with the Lagrangian taken in the form of pressure along with the scalar Clebsch potential as a dynamic variable. The dark energy is associated with a single scalar field with a potential which is hold unspecified as long as the theory permits. Both the Lagrangians of the dark matter and the scalar field are formulated in terms of the field variables which play a role of generalized coordinates in the Lagrangian formalism. It allows us to implement the powerful methods of variational calculus to derive the gauge-invariant field equations of the post-Newtonian celestial mechanics of an isolated astronomical system in an expanding universe. These equations generalize the field equations of the post-Newtonian theory in asymptotically flat spacetime by taking into account the cosmological effects explicitly and in a self-consistent manner without assuming the principle of liner superposition of the fields or a vacuole model of the isolated system, etc. The field equations for matter dynamic variables and gravitational field perturbations are coupled in the most general case of an arbitrary equation of state of matter of the background universe. We introduce a new cosmological gauge which generalizes the de Donder (harmonic) gauge of the post-Newtonian theory in asymptotically flat spacetime. This gauge significantly simplifies the gravitational field equations and allows one to find out the approximations where the field equations can be fully decoupled and solved analytically. The residual gauge freedom is explored and the residual gauge transformations are formulated in the form of the wave equations for the gauge functions. We demonstrate how the cosmological effects interfere with the local system and affect the local distribution of matter of the isolated system and its orbital dynamics. Finally, we worked out the precise mathematical definition of the Newtonian limit for an isolated system residing on the cosmological manifold. The results of the present paper can be useful in the Solar System for calculating more precise ephemerides of the Solar System bodies on extremely long time intervals, in galactic astronomy to study the dynamics of clusters of galaxies, and in gravitational wave astronomy for discussing the impact of cosmology on generation and propagation of gravitational waves emitted by coalescing binaries and/or merging galactic nuclei.

On the validity of the modified equation approach to the stability analysis of finite-difference methods

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1987-01-01

The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material.

PubMed

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-04-13

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10 -4 -10 -2 s -1 ) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations.

Quantum mechanics of conformally and minimally coupled Friedmann-Robertson-Walker cosmology

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

1992-10-01

The expansion method by a time-dependent basis of the eigenfunctions for the space-coordinate-dependent sub-Hamiltonian is one of the most natural frameworks for quantum systems, relativistic as well as nonrelativistic. The complete set of wave functions is found in the product integral formulation, whose constants of integration are fixed by Cauchy initial data. The wave functions for the Friedmann-Robertson-Walker (FRW) cosmology conformally and minimally coupled to a scalar field with a power-law potential or a polynomial potential are expanded in terms of the eigenfunctions of the scalar field sub-Hamiltonian part. The resultant gravitational field part which is an ``intrinsic'' timelike variable-dependent matrix-valued differential equation is solved again in the product integral formulation. There are classically allowed regions for the ``intrinsic'' timelike variable depending on the scalar field quantum numbers and these regions increase accordingly as the quantum numbers increase. For a fixed large three-geometry the wave functions corresponding to the low excited (small quantum number) states of the scalar field are exponentially damped or diverging and the wave functions corresponding to the high excited (large quantum number) states are still oscillatory but become eventually exponential as the three-geometry becomes larger. Furthermore, a proposal is advanced that the wave functions exponentially damped for a large three-geometry may be interpreted as ``tunneling out'' wave functions into, and the wave functions exponentially diverging as ``tunneling in'' from, different universes with the same or different topologies, the former being interpreted as the recently proposed Hawking-Page wormhole wave functions. It is observed that there are complex as well as Euclidean actions depending on the quantum numbers of the scalar field part outside the classically allowed region both of the gravitational and scalar fields, suggesting the usefulness of complex geometry and complex trajectories. From the most general wave functions for the FRW cosmology conformally coupled to scalar field, the boundary conditions for the wormhole wave functions are modified so that the modulus of wave functions, instead of the wave functions themselves, should be exponentially damped for a large three-geometry and be regular up to some negative power of the three-geometry as the three-geometry collapses. The wave functions for the FRW cosmology minimally coupled to an inhomogeneous scalar field are similarly found in the product integral formulation. The role of a large number of the inhomogeneous modes of the scalar field is not only to increase the classically allowed regions for the gravitational part but also to provide a mechanism of the decoherence of quantum interferences between the different sizes of the universe.

Massive graviton on arbitrary background: derivation, syzygies, applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernard, Laura; Deffayet, Cédric; IHES, Institut des Hautes Études Scientifiques,Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette

2015-06-23

We give the detailed derivation of the fully covariant form of the quadratic action and the derived linear equations of motion for a massive graviton in an arbitrary background metric (which were presented in arXiv:1410.8302 [hep-th]). Our starting point is the de Rham-Gabadadze-Tolley (dRGT) family of ghost free massive gravities and using a simple model of this family, we are able to express this action and these equations of motion in terms of a single metric in which the graviton propagates, hence removing in particular the need for a “reference metric' which is present in the non perturbative formulation. Wemore » show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. This last constraint involves powers and combinations of the curvature of the background metric. The 5 constraints are obtained for a background metric which is unconstrained, i.e. which does not have to obey the background field equations. We then apply these results to the case of Einstein space-times, where we show that the 5 constraints become trivial, and Friedmann-Lemaître-Robertson-Walker space-times, for which we correct in particular some results that appeared elsewhere. To reach our results, we derive several non trivial identities, syzygies, involving the graviton fields, its derivatives and the background metric curvature. These identities have their own interest. We also discover that there exist backgrounds for which the dRGT equations cannot be unambiguously linearized.« less

Massive graviton on arbitrary background: derivation, syzygies, applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernard, Laura; Deffayet, Cédric; Strauss, Mikael von, E-mail: bernard@iap.fr, E-mail: deffayet@iap.fr, E-mail: strauss@iap.fr

2015-06-01

We give the detailed derivation of the fully covariant form of the quadratic action and the derived linear equations of motion for a massive graviton in an arbitrary background metric (which were presented in arXiv:1410.8302 [hep-th]). Our starting point is the de Rham-Gabadadze-Tolley (dRGT) family of ghost free massive gravities and using a simple model of this family, we are able to express this action and these equations of motion in terms of a single metric in which the graviton propagates, hence removing in particular the need for a ''reference metric' which is present in the non perturbative formulation. Wemore » show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. This last constraint involves powers and combinations of the curvature of the background metric. The 5 constraints are obtained for a background metric which is unconstrained, i.e. which does not have to obey the background field equations. We then apply these results to the case of Einstein space-times, where we show that the 5 constraints become trivial, and Friedmann-Lemaître-Robertson-Walker space-times, for which we correct in particular some results that appeared elsewhere. To reach our results, we derive several non trivial identities, syzygies, involving the graviton fields, its derivatives and the background metric curvature. These identities have their own interest. We also discover that there exist backgrounds for which the dRGT equations cannot be unambiguously linearized.« less

Criticality and big brake singularities in the tachyonic evolutions of closed Friedmann universes with cold dark matter

NASA Astrophysics Data System (ADS)

Horváth, Zsolt; Keresztes, Zoltán; Kamenshchik, Alexander Yu.; Gergely, László Á.

2015-05-01

The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to 1 σ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudotachyonic regime into a sudden future singularity. Critical evolutions leading to big brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized by singularity avoidance in the pseudotachyon regime is presented.

Dynamics with infinitely many time derivatives in Friedmann-Robertson-Walker background and rolling tachyons

NASA Astrophysics Data System (ADS)

Joukovskaya, Liudmila

2009-02-01

Dynamics with infinitely many time derivatives has place in string field theory and have been profoundly investigated there. Recently there has been considerable interest in theories with infinitely many derivatives in the cosmological context in view of new features which these theories might accommodate owing to nonlocal interaction. In present work we continue investigation of such models, as a concrete example we study the dynamics of unstable D-brane in the open string theory in the Friedmann-Robertson-Walker background. We construct numerical solutions describing dynamical interpolation between the perturbative and non-perturbative vacua. The obtained solutions have several interesting properties and might be of interest from the cosmological points of view.

The modified semi-discrete two-dimensional Toda lattice with self-consistent sources

NASA Astrophysics Data System (ADS)

Gegenhasi

2017-07-01

In this paper, we derive the Grammian determinant solutions to the modified semi-discrete two-dimensional Toda lattice equation, and then construct the semi-discrete two-dimensional Toda lattice equation with self-consistent sources via source generation procedure. The algebraic structure of the resulting coupled modified differential-difference equation is clarified by presenting its Grammian determinant solutions and Casorati determinant solutions. As an application of the Grammian determinant and Casorati determinant solution, the explicit one-soliton and two-soliton solution of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources are given. We also construct another form of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources which is the Bäcklund transformation for the semi-discrete two-dimensional Toda lattice equation with self-consistent sources.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material

PubMed Central

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-01-01

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173–1573 K) and strain rates (10−4–10−2 s−1) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations. PMID:28772767

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunes, Rafael C.; Abreu, Everton M.C.; Neto, Jorge Ananias

Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. The effect of these non-gaussian statistics in the cosmological context is to change the strength of the gravitational constant. In this paper, we consider the w CDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modificationmore » with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we will use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data. We show that Tsallis' statistics is favored at 1σ confidence level.« less

BOOK REVIEW: Einsteins Kosmos. Untersuchungen zur Geschichte der Kosmologie Relativitatstheorie und zu Einsteins Wirken und Nachwirken

NASA Astrophysics Data System (ADS)

Sterken, C.; Duerbeck, H. W.; Dick, W. R.

2006-12-01

This book collects about 15 papers (most of them by one single author) on Einstein and the history of general relativity (GR) and the foundations of relativistic cosmology. The matter not only deals with Einstein and his times, but also with pre-GR ideas, and with the interplay of Einstein and his colleagues (opposing as well as supporting personalities). As the title indicates, all papers are written in German, but they include comprehensive Abstracts both in German and English. The book is illustrated with quite a number classical - but also some far more original though not less beautiful - photographs and facsimiles of documents. The book is edited very well, though the style of references is not quite homogeneous. There is no Index. K. Hentschel covers Einstein's argumentation for the existence of graviational redshift, and the initial search for empirical support. The error analysis of observational evidence supporting relativistic light deflection is discussed in a paper by P. Brosche. In particular, H. Duerbeck and P. Flin - in their description of the life and work of Silberstein, who was quite sceptic on the significance of the observational verifications a la Eddington - include the transcription of two most revealing letters by Silberstein to Sommerfeld (1919) and to Einstein (1934). In the first letter, Silberstein clearly shows his scientific maturity and integrity by scrutinising the observational evidence supporting light deflection, presented at a joint meeting of the Royal Society and the Royal Astronomical Society. The second letter, which is more a personal letter, includes lots of political references and connotations. Some of Einstein's political views are also revealed by D.B. Herrmann on the basis of his own correspondence with E.G. Straus, a collaborator of Einstein's. In a consequent paper, S. Grundmann gives remarks on Herrmann's contribution and illustrates Einstein's attitude towards Marx, Engels, Lenin and Stalin. M. Schemmel discusses Schwarzschild's cosmological speculations, and wonders why some people do immediately grasp the meaning and consequence of newly proposed doctrines, whereas the bulk of the contemporaneous scientists respond in a rather low profile. T. Jung reviews Einstein's contribution to cosmology, leading to the Friedmann-Einstein and Einstein-de Sitter universes (with a detailed Appendix on the Friedmann-Lemaitre cosmology), and also presents the cosmological work of Selety, and his correspondence with Einstein. In a subsequent paper, H.-J. Schmidt comments on Einstein's criticism on de Sitter's solution of the Einstein field equations. Controversies with Einstein are elaborated by G. Singer (on Friedmann) and by K. Roessler (on Lemaitre). J. Renn and T. Sauer discuss Mandl's role in the publication history of Einstein's papers, notably Einstein's short paper on gravitational lensing. Finally, the book concludes with a contribution by D.B. Herrmann about the relationship between Einstein and Archenhold Observatory (where Einstein gave his first Berlin popular lecture in 1915), the transcription of H.-J. Treder's 1979 public address at the Einstein memorial plaque, and an inventory list of about 50 Einstein memorabilia - monuments, busts, plaques - compiled by W.R. Dick. This book is based on ideas approached in a historical context from the individual perspective of the authors. It is a real treasure trove of information and basic references on the history of GR, and it also covers quite some grounds with mathematical equations.

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

Rigorous theoretical constraint on constant negative EoS parameter [Formula: see text] and its effect for the late Universe.

PubMed

Burgazli, Alvina; Eingorn, Maxim; Zhuk, Alexander

In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Supposing that the Universe contains also the cosmological constant and a perfect fluid with a negative constant equation of state (EoS) parameter [Formula: see text] (e.g., quintessence, phantom or frustrated network of topological defects), we investigate scalar perturbations of the Friedmann-Robertson-Walker metrics due to inhomogeneities. Our analysis shows that, to be compatible with the theory of scalar perturbations, this perfect fluid, first, should be clustered and, second, should have the EoS parameter [Formula: see text]. In particular, this value corresponds to the frustrated network of cosmic strings. Therefore, the frustrated network of domain walls with [Formula: see text] is ruled out. A perfect fluid with [Formula: see text] neither accelerates nor decelerates the Universe. We also obtain the equation for the nonrelativistic gravitational potential created by a system of inhomogeneities. Due to the perfect fluid with [Formula: see text], the physically reasonable solutions take place for flat, open and closed Universes. This perfect fluid is concentrated around the inhomogeneities and results in screening of the gravitational potential.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ip, Hiu Yan; Schmidt, Fabian, E-mail: iphys@mpa-garching.mpg.de, E-mail: fabians@mpa-garching.mpg.de

Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the 'separate universe' paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effectsmore » are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation of Hui and Bertschinger [1]. We also show that this very simple set of equations matches the exact evolution of the density field at second order, but fails at third and higher order. This provides a useful, easy-to-use framework for computing the fully relativistic growth of structure at second order.« less

Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piattella, O.F.; Rodrigues, D.C.; Fabris, J.C.

2013-11-01

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ{sub 1D}{sup 2}){sup 3/2} remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ''observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-spacemore » density indicator: λ{sub J} = (5π/G){sup 1/2}Q{sup −1/3}ρ{sub dm}{sup −1/6}. The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10{sup −6}M{sub ⊙}.« less

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marra, Valerio; Kolb, Edward W.; Matarrese, Sabino

We analyze a toy Swiss-cheese cosmological model to study the averaging problem. In our Swiss-cheese model, the cheese is a spatially flat, matter only, Friedmann-Robertson-Walker solution (i.e., the Einstein-de Sitter model), and the holes are constructed from a Lemaitre-Tolman-Bondi solution of Einstein's equations. We study the propagation of photons in the Swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the expansion scalar is unaffected by the inhomogeneities (i.e., the phenomenological homogeneous model is the cheese model). This is because of the spherical symmetry of the model;more » it is unclear whether the expansion scalar will be affected by nonspherical voids. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the {lambda}CDM concordance model. It is interesting that, although the sole source in the Swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological homogeneous model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w{sub 0} and w{sub a} follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that, within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.« less

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Invariant quantities in the scalar-tensor theories of gravitation

NASA Astrophysics Data System (ADS)

Järv, Laur; Kuusk, Piret; Saal, Margus; Vilson, Ott

2015-01-01

We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lemaître-Robertson-Walker cosmology in Einstein and Jordan frames and explain their correspondence despite the approximate equations turning out to be linear and nonlinear in different frames.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marra, Valerio; Kolb, Edward W.; Matarrese, Sabino

Photon geodesics are calculated in a Swiss-cheese model, where the cheese is made of the usual Friedmann-Robertson-Walker (FRW) solution and the holes are constructed from a Lemaitre-Tolman-Bondi solution of Einstein's equations. The observables on which we focus are the changes in the redshift, in the angular-diameter-distance relation, in the luminosity-distance-redshift relation, and in the corresponding distance modulus. We find that redshift effects are suppressed when the hole is small because of a compensation effect acting on the scale of half a hole resulting from the special case of spherical symmetry. However, we find interesting effects in the calculation of themore » angular distance: strong evolution of the inhomogeneities (as in the approach to caustic formation) causes the photon path to deviate from that of the FRW case. Therefore, the inhomogeneities are able to partly mimic the effects of a dark-energy component. Our results also suggest that the nonlinear effects of caustic formation in cold dark matter models may lead to interesting effects on photon trajectories.« less

Scalar field quantum cosmology: A Schrödinger picture

NASA Astrophysics Data System (ADS)

Vakili, Babak

2012-11-01

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.

Generalized second law of thermodynamics in f(T,TG) gravity

NASA Astrophysics Data System (ADS)

Zubair, M.; Jawad, Abdul

2015-11-01

We discuss the equilibrium picture of thermodynamic at the apparent horizon of FRW universe in f(T,TG) gravity, where T represents the torsion invariant and TG is the teleparallel equivalent of the Gauss-Bonnet term. It is found that one can translate the Friedmann equations to the standard form of first law of thermodynamics. We discuss GSLT in the locality of assumption that temperature of matter inside the horizon is similar to that of apparent horizon. Furthermore, we consider particular models in this theory and generate constraints on the coupling parameters for the validity of GSLT. For this purpose we set the present day values of cosmic parameters and find the possible constraints on f(T,TG) models. We also choose the power law cosmology and found that GSLT can be met in accelerated cosmic expansion. We have also presented the cosmological reconstruction of some viable f(T,TG) models and discussed the cosmic evolution and validity of GSLT.

The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function. [galaxy distribution

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1979-01-01

The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.

Brane with variable tension as a possible solution to the problem of the late cosmic acceleration

NASA Astrophysics Data System (ADS)

García-Aspeitia, Miguel A.; Hernandez-Almada, A.; Magaña, Juan; Amante, Mario H.; Motta, V.; Martínez-Robles, C.

2018-05-01

Braneworld models have been proposed as a possible solution to the problem of the accelerated expansion of the Universe. The idea is to dispense the dark energy (DE) and drive the late-time cosmic acceleration with a five-dimensional geometry. We investigate a brane model with variable brane tension as a function of redshift called chrono-brane. We propose the polynomial λ =(1 +z )n function inspired in tracker-scalar-field potentials. To constrain the n exponent we use the latest observational Hubble data from cosmic chronometers, Type Ia Supernovae from the full joint-light-analysis sample, baryon acoustic oscillations and the posterior distance from the cosmic microwave background of Planck 2015 measurements. A joint analysis of these data estimates n ≃6.19 ±0.12 which generates a DE-like (cosmological-constantlike at late times) term, in the Friedmann equation arising from the extra dimensions. This model is consistent with these data and can drive the Universe to an accelerated phase at late times.

Effects of anisotropy and spatial curvature on the pre-big-bang scenario

NASA Astrophysics Data System (ADS)

Clancy, Dominic; Lidsey, James E.; Tavakol, Reza

1998-08-01

A class of exact, anisotropic cosmological solutions to the vacuum Brans-Dicke theory of gravity is considered within the context of the pre-big-bang scenario. Included in this class are the Bianchi type III, V and VIh models and the spatially isotropic, negatively curved Friedmann-Robertson-Walker universe. The effects of large anisotropy and spatial curvature are determined. In contrast with a negatively curved Friedmann-Robertson-Walker model, there exist regions of the parameter space in which the combined effects of curvature and anisotropy prevent the occurrence of inflation. When inflation is possible, the necessary and sufficient conditions for successful pre-big-bang inflation are more stringent than in the isotropic models. The initial state for these models is established and corresponds in general to a gravitational plane wave.

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

NASA Astrophysics Data System (ADS)

Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot

2018-05-01

The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.

Unified approach for incompressible flows

NASA Astrophysics Data System (ADS)

Chang, Tyne-Hsien

1993-12-01

An unified approach for solving both compressible and incompressible flows was investigated in this study. The difference in CFD code development between incompressible and compressible flows is due to the mathematical characteristics. However, if one can modify the continuity equation for incompressible flows by introducing pseudocompressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of a compressible flow code to solve incompressible flows becomes feasible. Among numerical algorithms developed for compressible flows, the Centered Total Variation Diminishing (CTVD) schemes possess better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that CTVD schemes can equally well solve incompressible flows. In this study, the governing equations for incompressible flows include the continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the boundary conditions including physical and numerical boundary conditions must be properly specified to obtain accurate solution. The CFD code for this research is currently in progress. Flow past a circular cylinder will be used for numerical experiments to determine the accuracy and efficiency of the code before applying this code to more specific applications.

A discrete model of a modified Burgers' partial differential equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.; Shoosmith, J. N.

1990-01-01

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State

NASA Astrophysics Data System (ADS)

Speck, Jared

2013-07-01

In this article, we study the 1 + 3-dimensional relativistic Euler equations on a pre-specified conformally flat expanding spacetime background with spatial slices that are diffeomorphic to {R}^3. We assume that the fluid verifies the equation of state {p = c2s ρ,} where {0 ≤ cs ≤ √{1/3}} is the speed of sound. We also assume that the reciprocal of the scale factor associated with the expanding spacetime metric verifies a c s -dependent time-integrability condition. Under these assumptions, we use the vector field energy method to prove that an explicit family of physically motivated, spatially homogeneous, and spatially isotropic fluid solutions are globally future-stable under small perturbations of their initial conditions. The explicit solutions corresponding to each scale factor are analogs of the well-known spatially flat Friedmann-Lemaître-Robertson-Walker family. Our nonlinear analysis, which exploits dissipative terms generated by the expansion, shows that the perturbed solutions exist for all future times and remain close to the explicit solutions. This work is an extension of previous results, which showed that an analogous stability result holds when the spacetime is exponentially expanding. In the case of the radiation equation of state p = (1/3)ρ, we also show that if the time-integrability condition for the reciprocal of the scale factor fails to hold, then the explicit fluid solutions are unstable. More precisely, we show the existence of an open family of initial data such that (i) it contains arbitrarily small smooth perturbations of the explicit solutions' data and (ii) the corresponding perturbed solutions necessarily form shocks in finite time. The shock formation proof is based on the conformal invariance of the relativistic Euler equations when {c2s = 1/3,} which allows for a reduction to a well-known result of Christodoulou.

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-08-01

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Expanding wave solutions of the Einstein equations that induce an anomalous acceleration into the Standard Model of Cosmology.

PubMed

Temple, Blake; Smoller, Joel

2009-08-25

We derive a system of three coupled equations that implicitly defines a continuous one-parameter family of expanding wave solutions of the Einstein equations, such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology is embedded as a single point in this family. By approximating solutions near the center to leading order in the Hubble length, the family reduces to an explicit one-parameter family of expanding spacetimes, given in closed form, that represents a perturbation of the Standard Model. By introducing a comoving coordinate system, we calculate the correction to the Hubble constant as well as the exact leading order quadratic correction to the redshift vs. luminosity relation for an observer at the center. The correction to redshift vs. luminosity entails an adjustable free parameter that introduces an anomalous acceleration. We conclude (by continuity) that corrections to the redshift vs. luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of this free parameter. The next order correction is then a prediction. Since nonlinearities alone could actuate dissipation and decay in the conservation laws associated with the highly nonlinear radiation phase and since noninteracting expanding waves represent possible time-asymptotic wave patterns that could result, we propose to further investigate the possibility that these corrections to the Standard Model might be the source of the anomalous acceleration of the galaxies, an explanation not requiring the cosmological constant or dark energy.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

NASA Astrophysics Data System (ADS)

Akbulut, Arzu; Taşcan, Filiz

2018-04-01

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

Analytic solution for the space-time fractional Klein-Gordon and coupled conformable Boussinesq equations

NASA Astrophysics Data System (ADS)

Shallal, Muhannad A.; Jabbar, Hawraz N.; Ali, Khalid K.

2018-03-01

In this paper, we constructed a travelling wave solution for space-time fractional nonlinear partial differential equations by using the modified extended Tanh method with Riccati equation. The method is used to obtain analytic solutions for the space-time fractional Klein-Gordon and coupled conformable space-time fractional Boussinesq equations. The fractional complex transforms and the properties of modified Riemann-Liouville derivative have been used to convert these equations into nonlinear ordinary differential equations.

On the cosmological gravitational waves and cosmological distances

NASA Astrophysics Data System (ADS)

Belinski, V. A.; Vereshchagin, G. V.

2018-03-01

We show that solitonic cosmological gravitational waves propagated through the Friedmann universe and generated by the inhomogeneities of the gravitational field near the Big Bang can be responsible for increase of cosmological distances.

Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2016-01-01

Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in)homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé-Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Superconducting dark energy

NASA Astrophysics Data System (ADS)

Liang, Shi-Dong; Harko, Tiberiu

2015-04-01

Based on the analogy with superconductor physics we consider a scalar-vector-tensor gravitational model, in which the dark energy action is described by a gauge invariant electromagnetic type functional. By assuming that the ground state of the dark energy is in a form of a condensate with the U(1) symmetry spontaneously broken, the gauge invariant electromagnetic dark energy can be described in terms of the combination of a vector and of a scalar field (corresponding to the Goldstone boson), respectively. The gravitational field equations are obtained by also assuming the possibility of a nonminimal coupling between the cosmological mass current and the superconducting dark energy. The cosmological implications of the dark energy model are investigated for a Friedmann-Robertson-Walker homogeneous and isotropic geometry for two particular choices of the electromagnetic type potential, corresponding to a pure electric type field, and to a pure magnetic field, respectively. The time evolutions of the scale factor, matter energy density and deceleration parameter are obtained for both cases, and it is shown that in the presence of the superconducting dark energy the Universe ends its evolution in an exponentially accelerating vacuum de Sitter state. By using the formalism of the irreversible thermodynamic processes for open systems we interpret the generalized conservation equations in the superconducting dark energy model as describing matter creation. The particle production rates, the creation pressure and the entropy evolution are explicitly obtained.

Solving Differential Equations Using Modified Picard Iteration

ERIC Educational Resources Information Center

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

The Analytic Structures of Dynamical Systems.

DTIC Science & Technology

1986-01-01

equations , rational solutions, and the Painlev6 property for the Kadomtsev - Petviashvili and Hirota-Satsuma equations ", J. Math. Phys. 26 2174 (1985) 5...of rational solutions. This also obtains the Lax pairs for the modified equations . In this paper we apply this method to the Kadomtsev - Petviashvili ...3 . . . . .. .. ," ,",,....". . ".’..’.-.: -.... ., Modified equations , rational solutions, and the Painlev6 property for the Kadomtsev

Growth of structure in the Szekeres class-II inhomogeneous cosmological models and the matter-dominated era

NASA Astrophysics Data System (ADS)

Ishak, Mustapha; Peel, Austin

2012-04-01

This study belongs to a series devoted to using the Szekeres inhomogeneous models in order to develop a theoretical framework where cosmological observations can be investigated with a wider range of possible interpretations. While our previous work addressed the question of cosmological distances versus redshift in these models, the current study is a start at looking into the growth rate of large-scale structure. The Szekeres models are exact solutions to Einstein’s equations that were originally derived with no symmetries. We use here a formulation of the Szekeres models that is due to Goode and Wainwright, who considered the models as exact perturbations of a Friedmann-Lemaître-Robertson-Walker (FLRW) background. Using the Raychaudhuri equation we write, for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact nonlinear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated cosmic era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres nonlinear perturbations. We also find that the Szekeres growth rate with an Einstein-de Sitter background is stronger than that of the well-known nonlinear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today.

The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

PubMed

Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef

2013-01-01

Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

PubMed

Kilic, Mustafa Sabri; Bazant, Martin Z; Ajdari, Armand

2007-02-01

In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these modified PNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari [Phys. Rev. E 70, 021506 (2004)] for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I [Kilic, Bazant, and Ajdari, Phys. Rev. E 75, 021502 (2007)] for such problems.

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Constraints on modified gravity models from white dwarfs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Srimanta; Singh, Tejinder P.; Shankar, Swapnil, E-mail: srimanta.banerjee@tifr.res.in, E-mail: swapnil.shankar@cbs.ac.in, E-mail: tpsingh@tifr.res.in

Modified gravity theories can introduce modifications to the Poisson equation in the Newtonian limit. As a result, we expect to see interesting features of these modifications inside stellar objects. White dwarf stars are one of the most well studied stars in stellar astrophysics. We explore the effect of modified gravity theories inside white dwarfs. We derive the modified stellar structure equations and solve them to study the mass-radius relationships for various modified gravity theories. We also constrain the parameter space of these theories from observations.

Holographic Dark Energy Density

NASA Astrophysics Data System (ADS)

Saadat, Hassan

2011-06-01

In this article we consider the cosmological model based on the holographic dark energy. We study dark energy density in Universe with arbitrary spatially curvature described by the Friedmann-Robertson-Walker metric. We use Chevallier-Polarski-Linder parametrization to specify dark energy density.

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kinney, William H., E-mail: whkinney@buffalo.edu

We consider observational limits on a proposed model of the string landscape in inflation. In this scenario, effects from the decoherence of entangled quantum states in long-wavelength modes in the universe result in modifications to the Friedmann Equation and a corresponding modification to inflationary dynamics. Previous work [1, 2] suggested that such effects could provide an explanation for well-known anomalies in the Cosmic Microwave Background (CMB), such as the lack of power on large scales and the ''cold spot'' seen by both the WMAP and Planck satellites. In this paper, we compute limits on these entanglement effects from the Planckmore » CMB data combined with the BICEP/Keck polarization measurement, and find no evidence for observable modulations to the power spectrum from landscape entanglement, and no sourcing of observable CMB anomalies. The originally proposed model with an exponential potential is ruled out to high significance. Assuming a Starobinsky-type R {sup 2} inflation model, which is consistent with CMB constraints, data place a 2σ lower bound of b > 6.46 × 10{sup 7} GeV on the Supersymmetry breaking scale associated with entanglement corrections.« less

The cosmological constant as an eigenvalue of a Sturm-Liouville problem

NASA Astrophysics Data System (ADS)

Astashenok, Artyom V.; Elizalde, Emilio; Yurov, Artyom V.

2014-01-01

It is observed that one of Einstein-Friedmann's equations has formally the aspect of a Sturm-Liouville problem, and that the cosmological constant, Λ, plays thereby the role of spectral parameter (what hints to its connection with the Casimir effect). The subsequent formulation of appropriate boundary conditions leads to a set of admissible values for Λ, considered as eigenvalues of the corresponding linear operator. Simplest boundary conditions are assumed, namely that the eigenfunctions belong to L 2 space, with the result that, when all energy conditions are satisfied, they yield a discrete spectrum for Λ>0 and a continuous one for Λ<0. A very interesting situation is seen to occur when the discrete spectrum contains only one point: then, there is the possibility to obtain appropriate cosmological conditions without invoking the anthropic principle. This possibility is shown to be realized in cyclic cosmological models, provided the potential of the matter field is similar to the potential of the scalar field. The dynamics of the universe in this case contains a sudden future singularity.

How does the cosmic large-scale structure bias the Hubble diagram?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fleury, Pierre; Clarkson, Chris; Maartens, Roy, E-mail: pierre.fleury@uct.ac.za, E-mail: chris.clarkson@qmul.ac.uk, E-mail: roy.maartens@gmail.com

2017-03-01

The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift matches the prediction of a Friedmann-Lemaître-Robertson-Walker model. However, the inhomogeneity of the Universe generically biases these observables, mainly due to peculiar velocities and gravitational lensing, in a way that depends on the notion of average used in theoretical calculations. In this article, we carefully derive the notion of average which corresponds to the observation of the Hubble diagram. We then calculate its bias at second-order in cosmological perturbations, and estimate the consequences on themore » inference of cosmological parameters, for various current and future surveys. We find that this bias deeply affects direct estimations of the evolution of the dark-energy equation of state. However, errors in the standard inference of cosmological parameters remain smaller than observational uncertainties, even though they reach percent level on some parameters; they reduce to sub-percent level if an optimal distance indicator is used.« less

Towards realistic singularity-free cosmological models

NASA Astrophysics Data System (ADS)

Senovilla, José M. M.

1996-02-01

We present an explicit general family of inhomogeneous cosmological models. The family contains an arbitrary function of comoving time (interpretable as the cosmological scale factor) and four arbitrary parameters. In general, it is a solution of Einstein's field equations for a fluid with anisotropic pressures, but it also includes a big subfamily of perfect-fluid metrics. The most interesting feature of this family is that it contains both all the diagonal separable singularity-free cosmological models recently found and all the Friedmann-Lemaître-Robertson-Walker standard models. This property allows one to speculate on the construction of some interesting models in which the Universe has been FLRW-like from some time on (for instance, since the nucleeosynthesis time), but it also went through primordial singularity-free inhomogeneous epochs (in fact, there are quite natural possibilities in which these primordial epochs are inflationary) without ever violating energy conditions or other physical properties. Nevertheless, the physical processes leading to the isotropization and homogenization of the Universe are not fixed nor indicated by the models themselves. The interesting properties of the general model are studied in some detail. ¢ 1996 The American Physical Society.

Towards cosmological dynamics from loop quantum gravity

NASA Astrophysics Data System (ADS)

Li, Bao-Fei; Singh, Parampreet; Wang, Anzhong

2018-04-01

We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC, causing a nonsingular bounce. Dynamics can be described by the Hamilton or Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one to one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the prebounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the postbounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.

General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

NASA Astrophysics Data System (ADS)

Zhu, Tao; Shu, Fu-Wen; Wu, Qiang; Wang, Anzhong

2012-02-01

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry Diff(M,F) to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet and infrared, but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.

Cosmological evolution as squeezing: a toy model for group field cosmology

NASA Astrophysics Data System (ADS)

Adjei, Eugene; Gielen, Steffen; Wieland, Wolfgang

2018-05-01

We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat Friedmann–Lemaître–Robertson–Walker universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton’s constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve as an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application.

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

NASA Astrophysics Data System (ADS)

Tang, Xiao-yan; Liang, Zu-feng; Hao, Xia-zhi

2018-07-01

A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a β-plane. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

Pavement-Transportation Computer Assisted Structural Engineering (PCASE) Implementation of the Modified Berggren (ModBerg) Equation for Computing the Frost Penetration Depth within Pavement Structures

DTIC Science & Technology

2012-04-01

ER D C/ G SL T R -1 2 -1 5 Pavement -Transportation Computer Assisted Structural Engineering (PCASE) Implementation of the Modified...Berggren (ModBerg) Equation for Computing the Frost Penetration Depth within Pavement Structures G eo te ch n ic al a n d S tr u ct u re s La b or at...April 2012 Pavement -Transportation Computer Assisted Structural Engineering (PCASE) Implementation of the Modified Berggren (ModBerg) Equation for

Topographical scattering of gravity waves

NASA Astrophysics Data System (ADS)

Miles, J. W.; Chamberlain, P. G.

1998-04-01

A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Ion-Conserving Modified Poisson-Boltzmann Theory Considering a Steric Effect in an Electrolyte

NASA Astrophysics Data System (ADS)

Sugioka, Hideyuki

2016-12-01

The modified Poisson-Nernst-Planck (MPNP) and modified Poisson-Boltzmann (MPB) equations are well known as fundamental equations that consider a steric effect, which prevents unphysical ion concentrations. However, it is unclear whether they are equivalent or not. To clarify this problem, we propose an improved free energy formulation that considers a steric limit with an ion-conserving condition and successfully derive the ion-conserving modified Poisson-Boltzmann (IC-MPB) equations that are equivalent to the MPNP equations. Furthermore, we numerically examine the equivalence by comparing between the IC-MPB solutions obtained by the Newton method and the steady MPNP solutions obtained by the finite-element finite-volume method. A surprising aspect of our finding is that the MPB solutions are much different from the MPNP (IC-MPB) solutions in a confined space. We consider that our findings will significantly contribute to understanding the surface science between solids and liquids.

Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions

NASA Astrophysics Data System (ADS)

Volchkov, Yu. M.

2017-09-01

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %.

Cosmology with a stiff matter era

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2015-11-01

We consider the possibility that the Universe is made of a dark fluid described by a quadratic equation of state P =K ρ2 , where ρ is the rest-mass density and K is a constant. The energy density ɛ =ρ c2+K ρ2 is the sum of two terms: a rest-mass term ρ c2 that mimics "dark matter" (P =0 ) and an internal energy term u =K ρ2=P that mimics a "stiff fluid" (P =ɛ ) in which the speed of sound is equal to the speed of light. In the early universe, the internal energy dominates and the dark fluid behaves as a stiff fluid (P ˜ɛ , ɛ ∝a-6). In the late universe, the rest-mass energy dominates and the dark fluid behaves as pressureless dark matter (P ≃0 , ɛ ∝a-3). We provide a simple analytical solution of the Friedmann equations for a universe undergoing a stiff matter era, a dark matter era, and a dark energy era due to the cosmological constant. This analytical solution generalizes the Einstein-de Sitter solution describing the dark matter era, and the Λ CDM model describing the dark matter era and the dark energy era. Historically, the possibility of a primordial stiff matter era first appeared in the cosmological model of Zel'dovich where the primordial universe is assumed to be made of a cold gas of baryons. A primordial stiff matter era also occurs in recent cosmological models where dark matter is made of relativistic self-gravitating Bose-Einstein condensates (BECs). When the internal energy of the dark fluid mimicking stiff matter is positive, the primordial universe is singular like in the standard big bang theory. It expands from an initial state with a vanishing scale factor and an infinite density. We consider the possibility that the internal energy of the dark fluid is negative (while, of course, its total energy density is positive), so that it mimics anti-stiff matter. This happens, for example, when the BECs have an attractive self-interaction with a negative scattering length. In that case, the primordial universe is nonsingular and bouncing like in loop quantum cosmology. At t =0 , the scale factor is finite and the energy density is equal to zero. The universe first has a phantom behavior where the energy density increases with the scale factor, then a normal behavior where the energy density decreases with the scale factor. For the sake of generality, we consider a cosmological constant of arbitrary sign. When the cosmological constant is positive, the Universe asymptotically reaches a de Sitter regime where the scale factor increases exponentially rapidly with time. This can account for the accelerating expansion of the Universe that we observe at present. When the cosmological constant is negative (anti-de Sitter), the evolution of the Universe is cyclic. Therefore, depending on the sign of the internal energy of the dark fluid and on the sign of the cosmological constant, we obtain analytical solutions of the Friedmann equations describing singular and nonsingular expanding, bouncing, or cyclic universes.

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=(±1,0)

NASA Astrophysics Data System (ADS)

Schmid, Christoph

2009-03-01

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein’s static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes.—The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity Ω→gyro of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B→g≡-2Ω→gyro. The gravitomagnetic field is caused by energy currents J→ɛ via the momentum constraint, Einstein’s G0^i^ equation, (-Δ+μ2)A→g=-16πGNJ→ɛ with B→g=curlA→g. This equation is analogous to Ampère’s law, but it holds for all time-dependent situations. Δ is the de Rham-Hodge Laplacian, and Δ=-curlcurl for the vorticity sector in Riemannian 3-space.—In the solution for an open universe the 1/r2-force of Ampère is replaced by a Yukawa force Yμ(r)=(-d/dr)[(1/R)exp⁡(-μr)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2πR is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and μ2=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein’s closed static universe.—We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.—We show that only energy currents in the toroidal vorticity sector with ℓ=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X→ℓm- has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions.—The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenböck formula for the difference between the de Rham-Hodge Laplacian Δ and the “rough” Laplacian ∇2 on vector fields.

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=({+-}1,0)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmid, Christoph

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein's static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes. -more » The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity {omega}-vector{sub gyro} of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B-vector{sub g}{identical_to}-2{omega}-vector{sub gyro}. The gravitomagnetic field is caused by energy currents J-vector{sub {epsilon}} via the momentum constraint, Einstein's G{sup 0-}circumflex{sub i-circumflex} equation, (-{delta}+{mu}{sup 2})A-vector{sub g}=-16{pi}G{sub N}J-vector{sub {epsilon}} with B-vector{sub g}=curl A-vector{sub g}. This equation is analogous to Ampere's law, but it holds for all time-dependent situations. {delta} is the de Rham-Hodge Laplacian, and {delta}=-curl curl for the vorticity sector in Riemannian 3-space. - In the solution for an open universe the 1/r{sup 2}-force of Ampere is replaced by a Yukawa force Y{sub {mu}}(r)=(-d/dr)[(1/R)exp(-{mu}r)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2{pi}R is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and {mu}{sup 2}=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein's closed static universe.--We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.--We show that only energy currents in the toroidal vorticity sector with l=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X-vector{sub lm}{sup -} has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions. - The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenboeck formula for the difference between the de Rham-Hodge Laplacian {delta} and the ''rough'' Laplacian {nabla}{sup 2} on vector fields.« less

a Numerical Comparison of Langrange and Kane's Methods of AN Arm Segment

NASA Astrophysics Data System (ADS)

Rambely, Azmin Sham; Halim, Norhafiza Ab.; Ahmad, Rokiah Rozita

A 2-D model of a two-link kinematic chain is developed using two dynamics equations of motion, namely Kane's and Lagrange Methods. The dynamics equations are reduced to first order differential equation and solved using modified Euler and fourth order Runge Kutta to approximate the shoulder and elbow joint angles during a smash performance in badminton. Results showed that Runge-Kutta produced a better and exact approximation than that of modified Euler and both dynamic equations produced better absolute errors.

Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong

2017-10-01

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.

Intermediate boundary conditions for LOD, ADI and approximate factorization methods

NASA Technical Reports Server (NTRS)

Leveque, R. J.

1985-01-01

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Dark Energy from structure: a status report

NASA Astrophysics Data System (ADS)

Buchert, Thomas

2008-02-01

The effective evolution of an inhomogeneous universe model in any theory of gravitation may be described in terms of spatially averaged variables. In Einstein’s theory, restricting attention to scalar variables, this evolution can be modeled by solutions of a set of Friedmann equations for an effective volume scale factor, with matter and backreaction source terms. The latter can be represented by an effective scalar field (“morphon field”) modeling Dark Energy. The present work provides an overview over the Dark Energy debate in connection with the impact of inhomogeneities, and formulates strategies for a comprehensive quantitative evaluation of backreaction effects both in theoretical and observational cosmology. We recall the basic steps of a description of backreaction effects in relativistic cosmology that lead to refurnishing the standard cosmological equations, but also lay down a number of challenges and unresolved issues in connection with their observational interpretation. The present status of this subject is intermediate: we have a good qualitative understanding of backreaction effects pointing to a global instability of the standard model of cosmology; exact solutions and perturbative results modeling this instability lie in the right sector to explain Dark Energy from inhomogeneities. It is fair to say that, even if backreaction effects turn out to be less important than anticipated by some researchers, the concordance high-precision cosmology, the architecture of current N-body simulations, as well as standard perturbative approaches may all fall short in correctly describing the Late Universe.

Implications, Consequences and Interpretations of Generalized Entropy in the Cosmological Setups

NASA Astrophysics Data System (ADS)

Moradpour, H.

2016-09-01

Recently, it was argued (Tsallis and Cirto, Eur. Phys. J. C 73, 2487 2013) that the total entropy of a gravitational system should be related to the volume of system instead of the system surface. Here, we show that this new proposal cannot satisfy the unified first law of thermodynamics and the Friedmans equation simultaneously, unless the effects of dark energy candidate on the horizon entropy are considered. In fact, our study shows that some types of dark energy candidate may admit this proposal. Some general properties of required dark energy are also addressed. Moreover, our investigation shows that this new proposal for entropy, while combined with the second law of thermodynamics (as the backbone of Verlinde's proposal), helps us in provideing a thermodynamic interpretation for the difference between the surface and bulk degrees of freedom which, according to Padmanabhan's proposal, leads to the emergence of spacetime and thus the universe expansion. In fact, our investigation shows that the entropy changes of system may be equal to the difference between the surface and bulk degrees of freedom falling from surface into the system volume. Briefly, our results signal us that this new proposal for entropy may be in agreement with the thermodynamics laws, the Friedmann equation, Padmanabhan's holographic proposal for the emergence of spacetime and therefore the universe expansion. In fact, this new definition of entropy may be used to make a bridge between Verlinde's and Padmanabhan's proposals.

General Relativity During the Great War

NASA Astrophysics Data System (ADS)

Trimble, Virginia L.

2016-01-01

Einstein's (and Hilbert's) equations saw light of day in the darkness of Berlin 1915, as is well known. Moving from this highlight to less conspicuous topics, we find Karl Schwarzschild's solution of those equations (1916) followed shortly by his death. On the observational and American front, Slipher's assemblage of galaxy radial velocities, begun in 1912 with M31, continued apace. Shapley was busily moving us out of the galactic center. Also at Mt. Wilson, Charles St. John looked for gravitational redshift in the solar spectrum in 1917 without firmly detecting it. Adams demonstrated the very low luminosities of Sirius B and 40 Eri B in 1914 (but his attempt at a redshift for the former came only in 1923). Perhaps least well known is that a handful of additional critical theoretical papers date from the war years and describe the Lense-Thirring effect, the Reissner-Nordstrom solution, and a charged solution with a cosmological constant (due to the even more obscure Friedrich Kottler). Some of these came out of neutral Holland, but Kottler served both at Ypres and on the Galician front. Interesting mixes of military service and relativistic contributions are also associated with the names of Friedmann, Le Lemaître, Weyl (of the tensor), Minkowski, Hubble, Flamm, Droste, and Kretschmann. Astronomers in neutral Denmark, Holland and (until 1917) the USA facilitated transmittal of astronomical observations and other news across the battle lines so that Schwarzschild received an obituary in Nature and Moseley one in Naturwissenschaften.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Dust Acoustic Solitary Waves in Saturn F-ring's Region

NASA Astrophysics Data System (ADS)

E. K., El-Shewy; M. I. Abo el, Maaty; H. G., Abdelwahed; M. A., Elmessary

2011-01-01

Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains has been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Kortewege-de Vries (KdV) equation. At the critical hot dusty plasma density Nh0, the KdV equation is not appropriate for describing the system. Hence, a set of stretched coordinates is considered to derive the modified KdV equation. It is found that the presence of hot and cold dust charge grains not only significantly modifies the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical hot dusty plasma density Nh0, neither KdV nor mKdV equation is appropriate for describing the DAWs. Therefore, a further modified KdV (fmKdV) equation is derived, which admits both soliton and double layer solutions.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

An entropy correction method for unsteady full potential flows with strong shocks

NASA Technical Reports Server (NTRS)

Whitlow, W., Jr.; Hafez, M. M.; Osher, S. J.

1986-01-01

An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation.

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Modified cable equation incorporating transverse polarization of neuronal membranes for accurate coupling of electric fields.

PubMed

Wang, Boshuo; Aberra, Aman S; Grill, Warren M; Peterchev, Angel V

2018-04-01

We present a theory and computational methods to incorporate transverse polarization of neuronal membranes into the cable equation to account for the secondary electric field generated by the membrane in response to transverse electric fields. The effect of transverse polarization on nonlinear neuronal activation thresholds is quantified and discussed in the context of previous studies using linear membrane models. The response of neuronal membranes to applied electric fields is derived under two time scales and a unified solution of transverse polarization is given for spherical and cylindrical cell geometries. The solution is incorporated into the cable equation re-derived using an asymptotic model that separates the longitudinal and transverse dimensions. Two numerical methods are proposed to implement the modified cable equation. Several common neural stimulation scenarios are tested using two nonlinear membrane models to compare thresholds of the conventional and modified cable equations. The implementations of the modified cable equation incorporating transverse polarization are validated against previous results in the literature. The test cases show that transverse polarization has limited effect on activation thresholds. The transverse field only affects thresholds of unmyelinated axons for short pulses and in low-gradient field distributions, whereas myelinated axons are mostly unaffected. The modified cable equation captures the membrane's behavior on different time scales and models more accurately the coupling between electric fields and neurons. It addresses the limitations of the conventional cable equation and allows sound theoretical interpretations. The implementation provides simple methods that are compatible with current simulation approaches to study the effect of transverse polarization on nonlinear membranes. The minimal influence by transverse polarization on axonal activation thresholds for the nonlinear membrane models indicates that predictions of stronger effects in linear membrane models with a fixed activation threshold are inaccurate. Thus, the conventional cable equation works well for most neuroengineering applications, and the presented modeling approach is well suited to address the exceptions.

On the modified intermediate long-wave equation

NASA Astrophysics Data System (ADS)

Naumkin, Pavel I.; Sánchez-Suárez, Isahi

2018-03-01

We consider the modified intermediate long-wave equation ut-∂xu3+1ϑux+VP∫R12ϑcoth(π(y-x)2ϑ)uyy(t,y)dy=0. We develop the factorization technique to study the large time asymptotics of solutions.

FRW solutions and holography from uplifted AdS/CFT systems

NASA Astrophysics Data System (ADS)

Dong, Xi; Horn, Bart; Matsuura, Shunji; Silverstein, Eva; Torroba, Gonzalo

2012-05-01

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to nonaccelerating Friedmann-Robertson-Walker. We present simple Friedmann-Robertson-Walker solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower-dimensional graviton, and a finite covariant entropy bound, but at late times the lower-dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.

Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology

NASA Astrophysics Data System (ADS)

Singh, Parampreet; Wilson-Ewing, Edward

2014-02-01

We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaître-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaître-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

The new Asian modified CKD-EPI equation leads to more accurate GFR estimation in Chinese patients with CKD.

PubMed

Wang, Jinghua; Xie, Peng; Huang, Jian-Min; Qu, Yan; Zhang, Fang; Wei, Ling-Ge; Fu, Peng; Huang, Xiao-Jie

2016-12-01

To verify whether the new Asian modified CKD-EPI equation improved the performance of original one in determining GFR in Chinese patients with CKD. A well-designed paired cohort was set up. Measured GFR (mGFR) was the result of 99m Tc-diethylene triamine pentaacetic acid ( 99m Tc-DTPA) dual plasma sample clearance method. The estimated GFR (eGFR) was the result of the CKD-EPI equation (eGFR1) and the new Asian modified CKD-EPI equation (eGFR2). The comparisons were performed to evaluate the superiority of the eGFR2 in bias, accuracy, precision, concordance correlation coefficient and the slope of regression equation and measure agreement. A total of 195 patients were enrolled and analyzed. The new Asian modified CKD-EPI equation improved the performance of the original one in bias and accuracy. However, nearly identical performance was observed in the respect of precision, concordance correlation coefficient, slope of eGFR against mGFR and 95 % limit of agreement. In the subgroup of GFR < 60 mL min -1 /1.73 m 2 , the bias of eGFR1 was less than eGFR2 but they have comparable precision and accuracy. In the subgroup of GFR > 60 mL min -1 /1.73 m 2 , eGFR2 performed better than eGFR1 in terms of bias and accuracy. The new Asian modified CKD-EPI equation can lead to more accurate GFR estimation in Chinese patients with CKD in general practice, especially in the higher GFR group.

Scattering from a cylindrical reflector: modified theory of physical optics solution.

PubMed

Yalçin, Ugur

2007-02-01

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cataneo, Matteo; Rapetti, David; Lombriser, Lucas

We refine the mass and environment dependent spherical collapse model of chameleon f ( R ) gravity by calibrating a phenomenological correction inspired by the parameterized post-Friedmann framework against high-resolution N -body simulations. We employ our method to predict the corresponding modified halo mass function, and provide fitting formulas to calculate the enhancement of the f ( R ) halo abundance with respect to that of General Relativity (GR) within a precision of ∼< 5% from the results obtained in the simulations. Similar accuracy can be achieved for the full f ( R ) mass function on the condition thatmore » the modeling of the reference GR abundance of halos is accurate at the percent level. We use our fits to forecast constraints on the additional scalar degree of freedom of the theory, finding that upper bounds competitive with current Solar System tests are within reach of cluster number count analyses from ongoing and upcoming surveys at much larger scales. Importantly, the flexibility of our method allows also for this to be applied to other scalar-tensor theories characterized by a mass and environment dependent spherical collapse.« less

Modified Van der Waals equation and law of corresponding states

NASA Astrophysics Data System (ADS)

Zhong, Wei; Xiao, Changming; Zhu, Yongkai

2017-04-01

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.

Modified Bloch equations and spectral hole burning in solids

NASA Astrophysics Data System (ADS)

Asadullina, N. Ya; Asadullin, T. Ya; Asadullin, Ya Ya

2001-06-01

On the grounds of Bloch equations modified by taking into account the power dependence of the dispersion and damping parameters, we give general expressions for hole shapes burnt in the absorption and polarization spectra of the two-level systems. The general expressions are used for detailed numerical calculations of the hole shapes and hole widths in a concrete paramagnetic system (quartz with [AlO4]0 centres). This system earlier was studied experimentally and theoretically through the transient nutation and free induction decay methods. The results on the hole width in our modified-Bloch-equations model are in good qualitative agreement with the FID data.

Theoretical Astrophysics - Volume 3, Galaxies and Cosmology

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2002-12-01

1. Overview: galaxies and cosmology; 2. Galactic structure and dynamics; 3. Friedmann model of the universe; 4. Thermal history of the universe; 5. Structure formation; 6. Cosmic microwave background radiation; 7. Formation of baryonic structures; 8. Active galactic nuclei; 9. Intergalactic medium and absorption systems; 10. Cosmological observations.

Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method

NASA Astrophysics Data System (ADS)

Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj

2017-11-01

This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.

Detection the nonlinear ultrasonic signals based on modified Duffing equations

NASA Astrophysics Data System (ADS)

Zhang, Yuhua; Mao, Hanling; Mao, Hanying; Huang, Zhenfeng

The nonlinear ultrasonic signals, like second harmonic generation (SHG) signals, could reflect the nonlinearity of material induced by fatigue damage in nonlinear ultrasonic technique which are weak nonlinear signals and usually submerged by strong background noise. In this paper the modified Duffing equations are applied to detect the SHG signals relating to the fatigue damage of material. Due to the Duffing equation could only detect the signal with specific frequency and initial phase, firstly the frequency transformation is carried on the Duffing equation which could detect the signal with any frequency. Then the influence of initial phases of to-be-detected signal and reference signal on the detection result is studied in detail, four modified Duffing equations are proposed to detect actual engineering signals with any initial phase. The relationship between the response amplitude and the total driving force is applied to estimate the amplitude of weak periodic signal. The detection results show the modified Duffing equations could effectively detect the second harmonic in SHG signals. When the SHG signals include strong background noise, the noise doesn't change the motion state of Duffing equation and the second harmonic signal could be detected until the SNR of noisy SHG signals are -26.3, yet the frequency spectrum method could only identify when the SNR is greater than 0.5. When estimation the amplitude of second harmonic signal, the estimation error of Duffing equation is obviously less than the frequency spectrum analysis method under the same noise level, which illustrates the Duffing equation has the noise immune capacity. The presence of the second harmonic signal in nonlinear ultrasonic experiments could provide an insight about the early fatigue damage of engineering components.

Effects of halogenated aromatics/aliphatics and nitrogen(N)-heterocyclic aromatics on estimating the persistence of future pharmaceutical compounds using a modified QSAR model.

PubMed

Lim, Seung Joo; Fox, Peter

2014-02-01

The effects of halogenated aromatics/aliphatics and nitrogen(N)-heterocyclic aromatics on estimating the persistence of future pharmaceutical compounds were investigated using a modified half life equation. The potential future pharmaceutical compounds investigated were approximately 2000 pharmaceutical drugs currently undergoing the United States Food and Drug Administration (US FDA) testing. EPI Suite (BIOWIN) model estimates the fates of compounds based on the biodegradability under aerobic conditions. While BIOWIN considered the biodegradability of a compound only, the half life equation used in this study was modified by biodegradability, sorption and cometabolic oxidation. It was possible that the potential future pharmaceutical compounds were more accurately estimated using the modified half life equation. The modified half life equation considered sorption and cometabolic oxidation of halogenated aromatic/aliphatics and nitrogen(N)-heterocyclic aromatics in the sub-surface, while EPI Suite (BIOWIN) did not. Halogenated aliphatics in chemicals were more persistent than halogenated aromatics in the sub-surface. In addition, in the sub-surface environment, the fates of organic chemicals were much more affected by halogenation in chemicals than by nitrogen(N)-heterocyclic aromatics. © 2013.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less

The Modified Hartmann Potential Effects on γ-rigid Bohr Hamiltonian

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Nur Pratiwi, Beta

2018-04-01

In this paper, we present the solution of Bohr Hamiltonian in the case of γ-rigid for the modified Hartmann potential. The modified Hartmann potential was formed from the original Hartmann potential, consists of β function and θ function. By using the separation method, the three-dimensional Bohr Hamiltonian equation was reduced into three one-dimensional Schrodinger-like equation which was solved analytically. The results for the wavefunction were shown in mathematically, while for the binding energy was solved numerically. The numerical binding energy for the presence of the modified Hartmann potential is lower than the binding energy value in the absence of modified Hartmann potential effect.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Aspects of Integrability in One and Several Dimensions,

DTIC Science & Technology

1986-01-01

Kadomtsev - Petviashvili (KP) equation , the modified KdV to the modified KP, the non-linear Schr6d- inger to the Davey-Stewartson, etc. Furthermore...but a function de- noted in 20 by T12. This function also generates recursion operators in analogy with T. i % 61 4. THE KADOMTSEV - PETVIASHVILI EQUATION ...and its Appl., 19 L • 11 (1985). [41] Caudrey, P.J., Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation (preprint

A Study of Two-Equation Turbulence Models on the Elliptic Streamline Flow

NASA Technical Reports Server (NTRS)

Blaisdell, Gregory A.; Qin, Jim H.; Shariff, Karim; Rai, Man Mohan (Technical Monitor)

1995-01-01

Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

A DRBEM for steady infiltration from periodic semi-circular channels with two different types of roots distribution

NASA Astrophysics Data System (ADS)

Solekhudin, Imam; Sumardi

2017-05-01

In this study, problems involving steady Infiltration from periodic semicircular channels with root-water uptake function are considered. These problems are governed by Richards equation. This equation can be studied more conveniently by transforming the equation into a modified Helmholtz equation. In these problems, two different types of root-water uptake are considered. A dual reciprocity boundary element method (DRBEM) with a predictor-corrector scheme is used to solve the modified Helmholtz equation numerically. Using the solution obtained, numerical values of suction potential and root-water uptake function can be computed. In addition, amount of water absorbed by the different plant roots distribution can also be computed and compared.

Reconstructing f(R) modified gravity with dark energy parametrization

NASA Astrophysics Data System (ADS)

Morita, Masaaki; Takahashi, Hirotaka

2014-03-01

We demonstrate the reconstruction of f(R) modified gravity theory with late-time accelerated cosmic expansion. A second-order differential equation for Lagrangian density is obtained from the field equation, and is solved as a function of the cosmic scale factor in two cases. First we begin with the case of a wCDM cosmological model, in which a dark-energy equation-of-state parameter w is constant, for simplicity. Next we extend the method to a case in which the parameter w is epoch-dependent and is expressed as the Chevallier-Polarski-Linder parametrization. Thus we can represent Lagrangian density of f(R) modified gravity theory in terms of dark energy parameters.

Eisenhart lifts and symmetries of time-dependent systems

NASA Astrophysics Data System (ADS)

Cariglia, M.; Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2016-10-01

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in n + 2 dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaître and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

Computing general-relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

NASA Astrophysics Data System (ADS)

Bruni, Marco; Thomas, Daniel B.; Wands, David

2014-02-01

We present the first calculation of an intrinsically relativistic quantity, the leading-order correction to Newtonian theory, in fully nonlinear cosmological large-scale structure studies. Traditionally, nonlinear structure formation in standard ΛCDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent approximation to the Einstein equations, the first relativistic correction to the usual Newtonian scalar potential is a gravitomagnetic vector potential, giving rise to frame dragging. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in ΛCDM and examine its magnitude relative to the scalar potential, finding that the power spectrum of the vector potential is of the order 10-5 times the scalar power spectrum over the range of nonlinear scales we consider. On these scales the vector potential is up to two orders of magnitudes larger than the value predicted by second-order perturbation theory extrapolated to the same scales. We also discuss some possible observable effects and future developments.

Simple cosmological model with inflation and late times acceleration

NASA Astrophysics Data System (ADS)

Szydłowski, Marek; Stachowski, Aleksander

2018-03-01

In the framework of polynomial Palatini cosmology, we investigate a simple cosmological homogeneous and isotropic model with matter in the Einstein frame. We show that in this model during cosmic evolution, early inflation appears and the accelerating phase of the expansion for the late times. In this frame we obtain the Friedmann equation with matter and dark energy in the form of a scalar field with a potential whose form is determined in a covariant way by the Ricci scalar of the FRW metric. The energy density of matter and dark energy are also parameterized through the Ricci scalar. Early inflation is obtained only for an infinitesimally small fraction of energy density of matter. Between the matter and dark energy, there exists an interaction because the dark energy is decaying. For the characterization of inflation we calculate the slow roll parameters and the constant roll parameter in terms of the Ricci scalar. We have found a characteristic behavior of the time dependence of density of dark energy on the cosmic time following the logistic-like curve which interpolates two almost constant value phases. From the required numbers of N-folds we have found a bound on the model parameter.

Optical properties of the Einstein-de Sitter-Kasner universe

NASA Astrophysics Data System (ADS)

Landry, Sylvie; Dyer, Charles C.

1997-09-01

Most studies of gravitational lensing and their impact on observations concentrate on lensing structures which are bounded, that is, of some finite size in an otherwise reasonably smooth background universe. In this paper, we consider a model of the universe, the ``cheese slice'' universe, where the lensing is caused by very large scale structures: large slabs of alternating pure vacuum and Friedmann-Lemaı⁁tre-Robertson-Walker (FLRW) dust. The ray tracing problem is solved and shows that only the Kasner regions will introduce a bending in the beam as it propagates. The Kasner slices also introduce anisotropic redshift effects. The optical scalar equations are used as a tool to obtain the cross-sectional area and shape of the beam. All physical properties of a bundle of rays traveling through the cheese slice model are obtained analytically. The only nonanalytical result is the evaluation, in Kasner regions, of the time variable along the beam as a function of the affine parameter. Practical model results are obtained from a computer code. Multislice models are studied and the resulting impact on astronomical observations, which includes the introduction of shear and amplification, is demonstrated.

Inertial Mass from Spin Nonlinearity

NASA Astrophysics Data System (ADS)

Cohen, Marcus

The inertial mass of a Fermion shows up as chiral cross-coupling in its Dirac system. No scalar term can invariantly couple left and right chirality fields; the Dirac matrices must be spin tensors of mixed chirality. We show how such tensor couplings could arise from nonlinear mixing of four spinor fields, two representing the local electron fields and two inertial spinor fields sourced in the distant masses. We thus give a model that implements Mach's principle. Following Mendel Sachs,1 we let the inertial spinors factor the moving spacetime tetrads qα(x) and bar {q}α (x) that appear in the Dirac operator. The inertial spinors do more than set the spacetime "stage;" they are players in the chiral dynamics. Specifically, we show how the massive Dirac system arises as the envelope modulation equations coupling left and right chirality electron fields on a Friedmann universe via nonlinear "spin gratings" with the inertial spinor fields. These gratings implement Penrose's "mass-scatterings," which keep the null zig-zags of the bispinor wave function confined to a timelike world tube. Local perturbations to the inertial spinor fields appear in the Dirac system as Abelian and non-Abelian vector potentials.

De Sitter stability and coarse graining

NASA Astrophysics Data System (ADS)

Markkanen, T.

2018-02-01

We present a 4-dimensional back reaction analysis of de Sitter space for a conformally coupled scalar field in the presence of vacuum energy initialized in the Bunch-Davies vacuum. In contrast to the usual semi-classical prescription, as the source term in the Friedmann equations we use expectation values where the unobservable information hidden by the cosmological event horizon has been neglected i.e. coarse grained over. It is shown that in this approach the energy-momentum is precisely thermal with constant temperature despite the dilution from the expansion of space due to a flux of energy radiated from the horizon. This leads to a self-consistent solution for the Hubble rate, which is gradually evolving and at late times deviates significantly from de Sitter. Our results hence imply de Sitter space to be unstable in this prescription. The solution also suggests dynamical vacuum energy: the continuous flux of energy is balanced by the generation of negative vacuum energy, which accumulatively decreases the overall contribution. Finally, we show that our results admit a thermodynamic interpretation which provides a simple alternate derivation of the mechanism. For very long times the solutions coincide with flat space.

Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skrypnyk, T.

We construct a new family of quasigraded Lie algebras that admit the Kostant-Adler scheme. They coincide with special quasigraded deformations of twisted subalgebras of the loop algebras. Using them we obtain new hierarchies of integrable equations in partial derivatives which we call 'modified' non-Abelian Toda field hierarchies.

Solubility of 3-Caffeoylquinic Acid in Different Solvents at 291-340 K

NASA Astrophysics Data System (ADS)

Wang, Y. T.; Zhang, C. L.; Cheng, X. L.; Zhao, J. H.; Wang, L. C.

2017-12-01

Using a laser monitoring observation technique the solubilities of 3-caffeoylquinic acid in pure solvents, water, methanol, ethanol, 1-propanol, 1-butanol, and two mixed solvents, methanol + water, ethanol + water have been determined at temperature range from 291-340 K. The experimental data were correlated by the modified Apelblat equation, λ h equation, and ideal model. The calculated solubilities were turned out very consistent with the experimental results, and the modified Apelblat equation shows the best agreement.

Thermodynamic consistency test procedure using orthogonal collocation and the Peng-Robinson equation of state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamm, L.L.; Van Brunt, V.

The Christiansen and Fredenslund programs for calculating vapor-liquid equilibria have been modified by replacing the Soave-Redlich-Kwong equation of state with the newly developed Peng-Robinson equation of state. This modification was shown to be a decided improvement for high pressure systems, especially in the critical and upper retrograde regions. Thermodynamic consistency tests were developed and used to evaluate and compare calculated values from both the modified and unmodified programs with reported experimental data for several vapor-liquid systems.

Modifying Poisson equation for near-solute dielectric polarization and solvation free energy

NASA Astrophysics Data System (ADS)

Yang, Pei-Kun

2016-06-01

The dielectric polarization P is important for calculating the stability of protein conformation and the binding affinity of protein-protein/ligand interactions and for exploring the nonthermal effect of an external electric field on biomolecules. P was decomposed into the product of the electric dipole moment per molecule p; bulk solvent density Nbulk; and relative solvent molecular density g. For a molecular solute, 4πr2p(r) oscillates with the distance r to the solute, and g(r) has a large peak in the near-solute region, as observed in molecular dynamics (MD) simulations. Herein, the Poisson equation was modified for computing p based on the modified Gauss's law of Maxwell's equations, and the potential of the mean force was used for computing g. For one or two charged atoms in a water cluster, the solvation free energies of the solutes obtained by these equations were similar to those obtained from MD simulations.

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

NASA Astrophysics Data System (ADS)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Dynamics of viscous cosmologies in the full Israel-Stewart formalism

NASA Astrophysics Data System (ADS)

Lepe, Samuel; Otalora, Giovanni; Saavedra, Joel

2017-07-01

A detailed dynamical analysis for a bulk viscosity model in the full Israel-Stewart formalism for a spatially flat Friedmann-Robertson-Walker universe is performed. In our study we have considered the total cosmic fluid constituted by radiation, dark matter, and dark energy. The dark matter fluid is treated as an imperfect fluid which has a bulk viscosity that depends on its energy density in the usual form ξ (ρm)=ξ0ρm1 /2, whereas the other components are assumed to behave as perfect fluids with constant equation of state parameter. We show that the thermal history of the Universe is reproduced provided that the viscous coefficient satisfies the condition ξ0≪1 , either for a zero or a suitable nonzero coupling between dark energy and viscous dark matter. In this case, the final attractor is a dark-energy-dominated, accelerating universe, with an effective equation of state parameter in the quintessence-like, cosmological constant-like, or phantom-like regime, in agreement with observations. As our main result, we show that in order to obtain a viable cosmological evolution and at the same time alleviating the cosmological coincidence problem via the mechanism of scaling solution, an explicit interaction between dark energy and viscous dark matter seems inevitable. This result is consistent with the well-known fact that models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. Furthermore, by insisting on above, we show that in the present context a phantom nature of this interacting dark energy fluid is also favored.

On buffer layers as non-reflecting computational boundaries

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Turkel, Eli L.

1996-01-01

We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.

Family-oriented cardiac risk estimator: a Java web-based applet.

PubMed

Crouch, Michael A; Jadhav, Ashwin

2003-01-01

We developed a Java applet that calculates four different estimates of a person's 10-year risk for heart attack: (1) Estimate based on Framingham equation (2) Framingham equation estimate modified by C-reactive protein (CRP) level (3) Framingham estimate modified by family history of heart disease in parents or siblings (4) Framingham estimate modified by both CRP and family heart disease history. This web-based, family-oriented cardiac risk estimator uniquely considers family history and CRP while estimating risk.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Electron-acoustic Instability Simulated By Modified Zakharov Equations

NASA Astrophysics Data System (ADS)

Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.

We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.

Non-Commutative Rational Yang-Baxter Maps

NASA Astrophysics Data System (ADS)

Doliwa, Adam

2014-03-01

Starting from multidimensional consistency of non-commutative lattice-modified Gel'fand-Dikii systems, we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising from geometric crystals. Our approach works under additional condition of centrality of certain products of non-commuting variables. Then we apply such a restriction on the level of the Gel'fand-Dikii systems what allows to obtain non-autonomous (but with central non-autonomous factors) versions of the equations. In particular, we recover known non-commutative version of Hirota's lattice sine-Gordon equation, and we present an integrable non-commutative and non-autonomous lattice modified Boussinesq equation.

Dust acoustic solitary waves in a dusty plasma with two kinds of nonthermal ions at different temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorranian, Davoud; Sabetkar, Akbar

The nonlinear dust acoustic solitary waves in a dusty plasma with two nonthermal ion species at different temperatures is studied analytically. Using reductive perturbation method, the Kadomtsev-Petviashivili (KP) equation is derived, and the effects of nonthermal coefficient, ions temperature, and ions number density on the amplitude and width of soliton in dusty plasma are investigated. It is shown that the amplitude of solitary wave of KP equation diverges at critical points of plasma parameters. The modified KP equation is also derived, and from there, the soliton like solutions of modified KP equation with finite amplitude is extracted. Results show thatmore » generation of rarefactive or compressive solitary waves strongly depends on the number and temperature of nonthermal ions. Results of KP equation confirm that for different magnitudes of ions temperature (mass) and number density, mostly compressive solitary waves are generated in a dusty plasma. In this case, the amplitude of solitary wave is decreased, while the width of solitary waves is increased. According to the results of modified KP equation for some certain magnitudes of parameters, there is a condition for generation of an evanescent solitary wave in a dusty plasma.« less

Radiation reaction on a classical charged particle: a modified form of the equation of motion.

PubMed

Alcaine, Guillermo García; Llanes-Estrada, Felipe J

2013-09-01

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.

Radiation reaction on a classical charged particle: A modified form of the equation of motion

NASA Astrophysics Data System (ADS)

Alcaine, Guillermo García; Llanes-Estrada, Felipe J.

2013-09-01

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.

Modified Lippmann--Schwinger equations for two-body scattering theory with long-range interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prugovecki, E.; Zorbas, J.

Two kinds of modified Lippmann-Schwinger equations are derived for the case of long-range potentials. The equations of the first kind are homogeneous and are a direct result of the fact that the standard Lippmann-Schwinger equations do not hold when long-range forces are present. The equations of the second kind depend on the existence of an operator Z such that W/sub plus or minus /=s-lim exp(iHt)Z exp-(-iHot). A general recipe for constructing Z is given and ita computation is carried through for the case of asymptotically Coulombic potentials. The resulting equations are used to compare the long-range theory with the theorymore » with a space cutoff (i.e., screened potential) in the limit in which that cutoff is being removed. (auth)« less

The Acquisition of Chinese Relative Clauses: Contrasting Two Theoretical Approaches

ERIC Educational Resources Information Center

Hu, Shenai; Gavarró, Anna; Vernice, Mirta; Guasti, Maria Teresa

2016-01-01

This study examines the comprehension of relative clauses by Chinese-speaking children, and evaluates the validity of the predictions of the Dependency Locality Theory (Gibson, 1998, 2000) and the Relativized Minimality approach (Friedmann, Belletti & Rizzi, 2009). One hundred and twenty children from three to eight years of age were tested by…

Quantum effects in cosmology

NASA Astrophysics Data System (ADS)

Starobinskii, A. A.; Zel'Dovich, Ia. B.

1988-02-01

The present status of understanding of the early universe is reviewed, emphasizing the role of microphysics. It is argued that the inflationary stage appears to be eternal, and that the universe is not at all homogeneous, with an infinite number of Friedmann universes created from one maternal de Sitter universe. The problem of quantum unpredictability is discussed.

Production of Non-Canonical Sentences in Agrammatic Aphasia: Limits in Representation or Rule Application?

ERIC Educational Resources Information Center

Burchert, Frank; Meissner, Nadine; De Bleser, Ria

2008-01-01

The study reported here compares two linguistically informed hypotheses on agrammatic sentence production, the TPH [Friedmann, N., & Grodzinsky, Y. (1997). "Tense and agreement in agrammatic production: Pruning the syntactic tree." "Brain and Language," 56, 397-425.] and the DOP [Bastiaanse, R., & van Zonneveld, R. (2005). "Sentence production…

Working Memory in Aphasia: Theory, Measures, and Clinical Implications

ERIC Educational Resources Information Center

Wright, Heather Harris; Shisler, Rebecca J.

2005-01-01

Recently, researchers have suggested that deficits in working memory capacity contribute to language-processing difficulties observed in individuals with aphasia (e.g., I. Caspari, S. Parkinson, L. LaPointe, & R. Katz, 1998; R. A. Downey et al., 2004; N. Friedmann & A. Gvion, 2003; H. H. Wright, M. Newhoff, R. Downey, & S. Austermann, 2003). A…

Remarks on the general solution for the flat Friedmann universe with exponential scalar-field potential and dust

NASA Astrophysics Data System (ADS)

Andrianov, A. A.; Cannata, F.; Kamenshchik, A. Yu.

2012-11-01

We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails, and we discuss the reasons of this puzzling phenomenon.

The Redshifts in Relativity

ERIC Educational Resources Information Center

Singh, Satya Pal; Singh, Apoorva; Hareet, Prabhav

2011-01-01

The progress of modern cosmology took off in 1917 when A. Einstein published his paper on general theory of relativity extending his work of special theory of relativity (1905). In 1922 Alexander Friedmann constructed a mathematical model for expanding Universe that had a big bang in remote past. The experimental evidences could come in 1929 by…

Tense and Agreement Dissociations in German Agrammatic Speakers: Underspecification Vs. Hierarchy

ERIC Educational Resources Information Center

Burchert, F.; Swoboda-Moll, M.; Bleser, R.D.

2005-01-01

The aim of the present paper was to investigate whether German agrammatic production data are compatible with the Tree-Pruning-Hypothesis (TPH; Friedmann & Grodzinsky, 1997). The theory predicts unidirectional patterns of dissociation in agrammatic production data with respect to Tense and Agreement. However, there was evidence of a double…

BOOK REVIEW: The Wraparound Universe

NASA Astrophysics Data System (ADS)

Zakrzewski, Wojtek J.

2008-11-01

I thoroughly enjoyed reading this book. It is written in clear language supplemented with many very helpful photographs and drawings. I like the structure of the book, which is a collection of 45 rather short chapters that make it easier for the reader to read it at his/her own speed. The main aim of the author is to interest the reader in cosmology and to convey to him/her the amazing progress that has been made in recent years in our understanding of the universe, its shape and its future. However, even to formulate this problem and to describe some recent work in this field, the author has to explain to the reader many concepts from mathematics and physics. Jean-Pierre Luminet, in addition to being a well known astrophysicist, is also a very gifted writer and so he manages to do this very successfully. In fact the book contains very few formulae and most of the explanations are given in terms of a written narrative supplemented by drawings. The author is also extremely skillful in finding and then using appropriate analogies. The required ideas from mathematics, and topology in particular, present a further aim of the book—to explain to the interested reader the beautiful world of topology and its relevance to the description of the real world. Here, again, he succeeds very impressively. The central claim of the book is as follows: instead of a simple topology, the Universe may have a multiply-connected topology—hence 'wrapped around'; in consequence, it may be much smaller than is usually assumed. If this is so some of the galaxies we see are not real galaxies, but only images of a smaller number of genuine galaxies. The author then discusses possible topologies, and finally chooses the 'dodecahedral' one. A large part of the book is dedicated to showing how this hypothesis can be tested, and what the most recent data on the cosmic background radiation from the WMAP satellite say about this issue (they are inconclusive). Jean-Pierre Luminet's suggestions disagree with the standard inflationary model, which uses the same data to argue that the Universe is spatially flat, and so infinite. The author is also scrupulous in apportioning priorities. As he explains in detail in several historical sections, the standard cosmological equations (normally called Robertson Walker, or Friedmann Robertson Walker equations) were first written by Lemaitre and Friedmann—hence in the book the cosmological models which use them are always referred to as Friedmann Lemaitre models. Similarly, the Doppler effect becomes the Doppler Fizeau effect and Hubble's law is entitled Hubble Lemaitre. I also liked the sections of the book in which the author shows how the same ideas in different historic or geographic conditions have had different impacts on the development of science; some were ignored, some misunderstood and some considered more seriously than they deserved. All in all, 'The Wraparound Universe' is a great general-audience book and I recommend it unreservedly.

Unified approach for incompressible flows

NASA Astrophysics Data System (ADS)

Chang, Tyne-Hsien

1995-07-01

A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.

Unified approach for incompressible flows

NASA Technical Reports Server (NTRS)

Chang, Tyne-Hsien

1995-01-01

A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

NASA Technical Reports Server (NTRS)

Gray, Carl E., Jr.

1988-01-01

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation

NASA Astrophysics Data System (ADS)

Chang, Xiangke; Szmigielski, Jacek

2018-02-01

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem, the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds, as well as Toda-like sorting property.

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.

PubMed

Ma, Li-Yuan; Zhu, Zuo-Nong

2014-09-01

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.

eGFRs from Asian-modified CKD-EPI and Chinese-modified CKD-EPI equations were associated better with hypertensive target organ damage in the community-dwelling elderly Chinese: the Northern Shanghai Study.

PubMed

Ji, Hongwei; Zhang, Han; Xiong, Jing; Yu, Shikai; Chi, Chen; Bai, Bin; Li, Jue; Blacher, Jacques; Zhang, Yi; Xu, Yawei

2017-01-01

With increasing age, estimated glomerular filtration rate (eGFR) decline is a frequent manifestation and is strongly associated with other preclinical target organ damage (TOD). In literature, many equations exist in assessing patients' eGFR. However, these equations were mainly derived and validated in the population from Western countries, which equation should be used for risk stratification in the Chinese population remains unclear, as well as their comparison. Considering that TOD is a good marker for risk stratification in the elderly, in this analysis, we aimed to investigate whether the recent eGFR equations derived from Asian and Chinese are better associated with preclinical TOD than the other equations in elderly Chinese. A total of 1,599 community-dwelling elderly participants (age >65 years) in northern Shanghai were prospectively recruited from June 2014 to August 2015. Conventional cardiovascular risk factors were assessed, and hypertensive TOD including left ventricular mass index (LVMI), carotid-femoral pulse wave velocity (cf-PWV), carotid intima-media thickness (IMT), ankle-brachial index (ABI) and urine albumin to creatinine ratio (UACR) was evaluated for each participant. Participant's eGFR was calculated from the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI), Chinese-abbreviated MDRD (c-aMDRD), Asian-modified CKD-EPI (aCKD-EPI) equation and Chinese-modified CKD-EPI (cCKD-EPI) equation. In multivariate regression analysis, only eGFRs from aCKD-EPI were significantly and inversely associated with carotid IMT ( P =0.005). In multivariate logistic models, decreased eGFR from all the equations were significantly associated with lower ABI ( P <0.001), microalbuminuria ( P =0.02 to P <0.001) and increased cf-PWV ( P <0.001). Only decreased eGFRs from aCKD-EPI and cCKD-EPI equations were significantly associated with increased IMT (both crude P <0.05). In the receiver operator characteristic (ROC) analysis, only aCKD-EPI and cCKD-EPI equations presented significant associations with all the listed preclinical TODs ( P -value from <0.05 to <0.001). In community-dwelling elderly Chinese, eGFRs from aCKD-EPI and cCKD-EPI equations are better associated with preclinical TOD. aCKD-EPI and cCKD-EPI equations should be preferred when making risk assessment.

Applications of the modified Rydberg-Vinet equation-of-state to the lower mantle and core

NASA Astrophysics Data System (ADS)

Fang, Zheng-Hua

2016-01-01

A modified Rydberg-Vinet equation-of-state (mRV EOS) with an arbitrary nonzero-pressure reference point, as is derived strictly from the related Rydberg potential, has been applied to the mantle and the core. The tests and comparisons demonstrate that mRV EOS is superior to the reciprocal K-primed equation [see F. D. Stacey and P. M. Davis, Phys. Earth Planet. Inter. 142 (2004) 137] not only because of its higher fitting accuracy but also because it has fewer fitting parameters and is easier to use.

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

ERIC Educational Resources Information Center

Hwang, Chi-en; Cleary, T. Anne

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

Hydrologic Impacts of Oak Harvesting and Evaluation of the Modified Universal Soil Loss Equation

Treesearch

Charlette R. Epifanio; Michael J. Singer; Xiaohong Huang

1991-01-01

Two Sierra foothill watersheds were monitored to learn what effects selective oak removal would have on watershed hydrology and water quality. We also used the data to generate sediment rating curves and evaluate the modified universal soil loss equation (MUSLE). Annual sediment rating curves better accounted for the variability in precipitation events from year to...

A Riemann-Hilbert Approach for the Novikov Equation

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2016-09-01

We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.

Variational theorems for superimposed motions in elasticity, with application to beams

NASA Technical Reports Server (NTRS)

Doekmeci, M. C.

1976-01-01

Variational theorems are presented for a theory of small motions superimposed on large static deformations and governing equations for prestressed beams on the basis of 3-D theory of elastodynamics. First, the principle of virtual work is modified through Friedrichs's transformation so as to describe the initial stress problem of elastodynamics. Next, the modified principle together with a chosen displacement field is used to derive a set of 1-D macroscopic governing equations of prestressed beams. The resulting equations describe all the types of superimposed motions in elastic beams, and they include all the effects of transverse shear and normal strains, and the rotatory inertia. The instability of the governing equations is discussed briefly.

Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagmeijer, R.

1994-11-01

A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of themore » computational coordinates.« less

Acoustic power balance in lined ducts

NASA Technical Reports Server (NTRS)

Eversman, W.

1979-01-01

It is shown that the two common definitions of acoustic energy density and intensity in uniform unlined ducts carrying uniform flow are compatible to the extent that both energy densities can be used in an appropriate variational principle to derive the convected wave equation. When the duct walls are lined both energy densities must be modified to account for the wall energy density. This results in a new energy conservation equation which utilizes a modified definition of axial power and accounts for wall dissipation. Computations in specific cases demonstrate the validity of the modified acoustic energy relation.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

A new modification in the exponential rational function method for nonlinear fractional differential equations

NASA Astrophysics Data System (ADS)

Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-02-01

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

Dynamics and phenomenology of higher order gravity cosmological models

NASA Astrophysics Data System (ADS)

Moldenhauer, Jacob Andrew

2010-10-01

I present here some new results about a systematic approach to higher-order gravity (HOG) cosmological models. The HOG models are derived from curvature invariants that are more general than the Einstein-Hilbert action. Some of the models exhibit late-time cosmic acceleration without the need for dark energy and fit some current observations. The open question is that there are an infinite number of invariants that one could select, and many of the published papers have stressed the need to find a systematic approach that will allow one to study methodically the various possibilities. We explore a new connection that we made between theorems from the theory of invariants in general relativity and these cosmological models. In summary, the theorems demonstrate that curvature invariants are not all independent from each other and that for a given Ricci Segre type and Petrov type (symmetry classification) of the space-time, there exists a complete minimal set of independent invariants (a basis) in terms of which all the other invariants can be expressed. As an immediate consequence of the proposed approach, the number of invariants to consider is dramatically reduced from infinity to four invariants in the worst case and to only two invariants in the cases of interest, including all Friedmann-Lemaitre-Robertson-Walker metrics. We derive models that pass stability and physical acceptability conditions. We derive dynamical equations and phase portrait analyses that show the promise of the systematic approach. We consider observational constraints from magnitude-redshift Supernovae Type Ia data, distance to the last scattering surface of the Cosmic Microwave Background radiation, and Baryon Acoustic Oscillations. We put observational constraints on general HOG models. We constrain different forms of the Gauss-Bonnet, f(G), modified gravity models with these observations. We show some of these models pass solar system tests. We seek to find models that pass physical and observational constraints and give fits to the data that are almost as good as those of the standard Lambda-Cold-Dark-Matter model. Finding accelerating HOG models with late-time acceleration that pass physical acceptability conditions, solar system tests, and cosmological constraints will constitute serious contenders to explain cosmic acceleration.

Erratum: Erratum to: Thermodynamic implications of the gravitationally induced particle creation scenario

NASA Astrophysics Data System (ADS)

Saha, Subhajit; Mondal, Anindita

2018-04-01

We would like to rectify an error regarding the validity of the first law of thermodynamics (FLT) on the apparent horizon of a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate (see Sect. 3.1 of original article)

Double-Plate Penetration Equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

2000-01-01

This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.

Neutron stars in screened modified gravity: Chameleon versus dilaton

NASA Astrophysics Data System (ADS)

Brax, Philippe; Davis, Anne-Christine; Jha, Rahul

2017-04-01

We consider the scalar field profile around relativistic compact objects such as neutron stars for a range of modified gravity models with screening mechanisms of the chameleon and Damour-Polyakov types. We focus primarily on inverse power law chameleons and the environmentally dependent dilaton as examples of both mechanisms. We discuss the modified Tolman-Oppenheimer-Volkoff equation and then implement a relaxation algorithm to solve for the scalar profiles numerically. We find that chameleons and dilatons behave in a similar manner and that there is a large degeneracy between the modified gravity parameters and the neutron star equation of state. This is exemplified by the modifications to the mass-radius relationship for a variety of model parameters.

Density of Jatropha curcas Seed Oil and its Methyl Esters: Measurement and Estimations

NASA Astrophysics Data System (ADS)

Veny, Harumi; Baroutian, Saeid; Aroua, Mohamed Kheireddine; Hasan, Masitah; Raman, Abdul Aziz; Sulaiman, Nik Meriam Nik

2009-04-01

Density data as a function of temperature have been measured for Jatropha curcas seed oil, as well as biodiesel jatropha methyl esters at temperatures from above their melting points to 90 ° C. The data obtained were used to validate the method proposed by Spencer and Danner using a modified Rackett equation. The experimental and estimated density values using the modified Rackett equation gave almost identical values with average absolute percent deviations less than 0.03% for the jatropha oil and 0.04% for the jatropha methyl esters. The Janarthanan empirical equation was also employed to predict jatropha biodiesel densities. This equation performed equally well with average absolute percent deviations within 0.05%. Two simple linear equations for densities of jatropha oil and its methyl esters are also proposed in this study.

Stochastic modeling of stock price process induced from the conjugate heat equation

NASA Astrophysics Data System (ADS)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution

NASA Astrophysics Data System (ADS)

Demiray, Hilmi; El-Zahar, Essam R.

2018-04-01

We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

PubMed

ben-Avraham, D; Fokas, A S

2001-07-01

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

NASA Astrophysics Data System (ADS)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

A modified resistance equation for modeling underwater spark discharge with salinity and high pressure conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Pengfei; Roy, Subrata, E-mail: roy@ufl.edu

2014-05-07

This work investigates the performance of underwater spark discharge relating to bubble growth and decay under high pressure and with salinity conditions by introducing a modified form of the resistance equation. Here, we study salinity influence on circuit parameters by fitting the experimental data for which gap resistance is much larger in conductive water than in dielectric water. Accordingly, the resistance equation is modified by considering the influence of both plasma and its surrounding liquid. Thermal radiation effect of the bubble is also studied by comparing two different radiation models. Numerical results predict a larger bubble pressure for saline watermore » but a reduced size and a smaller bubble cycle at a greater water depth. Such study may be useful in many saltwater applications, including that for deep sea conditions.« less

Nonlinear Waves.

DTIC Science & Technology

1986-05-27

purposes will be the Korteweg-deVries (KdV) equation u, 6uu, u. , =0 (1) in one spatial dimension, and the Kadomtsev - Petviashvili (KP) equation (u, - 6uu...one temporal dimen- sion: the Modified Kadomtsev - Petviashvili II (MKPII), and Davey-Stewartson I (OSII) equation . The hyperoolic analogs of (1), (2...by introducing ’Ś an intermediate version of the equations associated with (1), an infinite family of conserva- Kadomtsev - Petviashvili equation

A modified Poisson-Boltzmann equation applied to protein adsorption.

PubMed

Gama, Marlon de Souza; Santos, Mirella Simões; Lima, Eduardo Rocha de Almeida; Tavares, Frederico Wanderley; Barreto, Amaro Gomes Barreto

2018-01-05

Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects. Copyright © 2017 Elsevier B.V. All rights reserved.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

Marginally outer trapped surfaces and symmetries

NASA Astrophysics Data System (ADS)

Carrasco, Alberto; Mars, Marc

2009-05-01

We study properties of outermost marginally outer trapped surfaces in slices of space-times possessing certain symmetries, like isometries, homotheties or conformal Killings. In particular, we find restrictions on these surfaces for the vector field generating the symmetry. As an application we give a result of non-existence of outermost marginally outer trapped surfaces in accelerated Friedmann-Lemaître-Roberson-Walker spacetimes.

A Fundamental Study in Nonlinear Aeroelastic Phenomena in Flapping Wing Micro Air Vehicles

DTIC Science & Technology

2008-11-30

Investigator: Peretz P. Friedmann Fran9ois-Xavier Bagnoud Professor Phone 734-763-2354; FAX 734-763-0578; Email peretzf@umich.edu Co-Principal...itiffamng / a. g -0.02 -0.03 -0.04. V V " Wnhoul dynamic stiffening . Present study using MARC Singh. 8, PhD. Thesis Jmyang » 1(2005) 2 4 6

Modified Peng-Robinson Equation of State for Pure and Mixture Refrigerants with R-32,R-125 and R-134a

NASA Astrophysics Data System (ADS)

Ll, Jin; Sato, Haruki; Watanabe, Koichi

On the basis of critically-evaluated thermodynamic property data among those recently published, a new Peng-Robinson equation of state for the HFC refrigerants,R-32,R-125 and R-134a,has be end eveloped so as to represent the VLE properties in the vapor-liquid coexisting phase at temperatures 223K-323K. In accord with a challenge to correlate the binary and/or ternary interatction parameters as functions of temperature, we have also applied the present modified Peng-Robinson equation of state to the promising alternative HFC refrigerant mixtures, i.e., R-32/125,R-32/134a and R-32/125/134a systems. The developed equation of state improves significantly its effectiveness for practical engineering property calculations at refrigerantion and air-conditioning industries in comparison with conventional Peng-Robinson equation.

Thermodynamics properties study of diatomic molecules with q-deformed modified Poschl-Teller plus Manning Rosen non-central potential in D dimensions using SUSYQM approach

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Pratiwi, B. N.

2016-04-01

D-dimensional Dirac equation of q-deformed modified Poschl-Teller plus Manning Rosen non-central potential was solved using supersymmetric quantum mechanics (SUSY QM). The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial part of D dimensional Dirac equation and the angular quantum numbers were obtained from angular part of D dimensional Dirac equation. The SUSY operators was used to generate the D dimensional relativistic wave functions both for radial and angular parts. In the non-relativistic limit, the relativistic energy equation was reduced to the non-relativistic energy. In the classical limit, the partition function of vibrational, the specific heat of vibrational, and the mean energy of vibrational of some diatomic molecules were calculated from the equation of non-relativistic energy with the help of error function and Mat-lab 2011.

Cosmological perturbations in teleparallel Loop Quantum Cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haro, Jaime, E-mail: jaime.haro@upc.edu

2013-11-01

Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator. In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce providedmore » by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation. In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.« less

Relational evolution of effectively interacting group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi

2017-03-01

We study the impact of effective interactions onto relationally evolving group field theory (GFT) condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.

Apparent cosmic acceleration from Type Ia supernovae

NASA Astrophysics Data System (ADS)

Dam, Lawrence H.; Heinesen, Asta; Wiltshire, David L.

2017-11-01

Parameters that quantify the acceleration of cosmic expansion are conventionally determined within the standard Friedmann-Lemaître-Robertson-Walker (FLRW) model, which fixes spatial curvature to be homogeneous. Generic averages of Einstein's equations in inhomogeneous cosmology lead to models with non-rigidly evolving average spatial curvature, and different parametrizations of apparent cosmic acceleration. The timescape cosmology is a viable example of such a model without dark energy. Using the largest available supernova data set, the JLA catalogue, we find that the timescape model fits the luminosity distance-redshift data with a likelihood that is statistically indistinguishable from the standard spatially flat Λ cold dark matter cosmology by Bayesian comparison. In the timescape case cosmic acceleration is non-zero but has a marginal amplitude, with best-fitting apparent deceleration parameter, q_{0}=-0.043^{+0.004}_{-0.000}. Systematic issues regarding standardization of supernova light curves are analysed. Cuts of data at the statistical homogeneity scale affect light-curve parameter fits independent of cosmology. A cosmological model dependence of empirical changes to the mean colour parameter is also found. Irrespective of which model ultimately fits better, we argue that as a competitive model with a non-FLRW expansion history, the timescape model may prove a useful diagnostic tool for disentangling selection effects and astrophysical systematics from the underlying expansion history.

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity frommore » general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.« less

Non-singular bounce transitions in the multiverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu

2013-11-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition tomore » another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.« less

Reconstruction of f(T)-gravity in the absence of matter

NASA Astrophysics Data System (ADS)

El Hanafy, W.; Nashed, G. G. L.

2016-06-01

We derive an exact f(T) gravity in the absence of ordinary matter in Friedmann-Robertson-Walker (FRW) universe, where T is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor {T}^{μ ν } of matter does not imply vanishing of the teleparallel torsion scalar, in contrast to general relativity, where the Ricci scalar vanishes. The theory provides an exponential ( inflationary) scale factor independent of the choice of the sectional curvature. In addition, the obtained f(T) acts just like cosmological constant in the flat space model. Nevertheless, it is dynamical in non-flat models. In particular, the open universe provides a decaying pattern of the f(T) contributing directly to solve the fine-tuning problem of the cosmological constant. The equation of state (EoS) of the torsion vacuum fluid has been studied in positive and negative Hubble regimes. We study the case when the torsion is made of a scalar field ( tlaplon) which acts as torsion potential. This treatment enables to induce a tlaplon field sensitive to the symmetry of the spacetime in addition to the reconstruction of its effective potential from the f(T) theory. The theory provides six different versions of inflationary models. The real solutions are mainly quadratic, the complex solutions, remarkably, provide Higgs-like potential.

Viscous cosmology for early- and late-time universe

NASA Astrophysics Data System (ADS)

Brevik, Iver; Grøn, Øyvind; de Haro, Jaume; Odintsov, Sergei D.; Saridakis, Emmanuel N.

From a hydrodynamicist’s point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review, we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy-Verlinde formula is affected by viscosity.

A Modified Benedict-Webb-Rubin Equation of State for the Thermodynamic Properties of R152a (1,1-difluoroethane)

NASA Astrophysics Data System (ADS)

Outcalt, Stephanie L.; McLinden, Mark O.

1996-03-01

A modified Benedict-Webb-Rubin (MBWR) equation of state has been developed for R152a (1,1-difluoroethane). The correlation is based on a selection of available experimental thermodynamic property data. Single-phase pressure-volume-temperature (PVT), heat capacity, and sound speed data, as well as second virial coefficient, vapor pressure, and saturated liquid and saturated vapor density data, were used with multi-property linear least-squares fitting to determine the 32 adjustable coefficients of the MBWR equation. Ancillary equations representing the vapor pressure, saturated liquid and saturated vapor densities, and the ideal gas heat capacity were determined. Coefficients for the equation of state and the ancillary equations are given. Experimental data used in this work covered temperatures from 162 K to 453 K and pressures to 35 MPa. The MBWR equation established in this work may be used to predict thermodynamic properties of R152a from the triple-point temperature of 154.56 K to 500 K and for pressures up to 60 MPa except in the immediate vicinity of the critical point.

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

A modified homotopy perturbation method and the axial secular frequencies of a non-linear ion trap.

PubMed

Doroudi, Alireza

2012-01-01

In this paper, a modified version of the homotopy perturbation method, which has been applied to non-linear oscillations by V. Marinca, is used for calculation of axial secular frequencies of a non-linear ion trap with hexapole and octopole superpositions. The axial equation of ion motion in a rapidly oscillating field of an ion trap can be transformed to a Duffing-like equation. With only octopole superposition the resulted non-linear equation is symmetric; however, in the presence of hexapole and octopole superpositions, it is asymmetric. This modified homotopy perturbation method is used for solving the resulting non-linear equations. As a result, the ion secular frequencies as a function of non-linear field parameters are obtained. The calculated secular frequencies are compared with the results of the homotopy perturbation method and the exact results. With only hexapole superposition, the results of this paper and the homotopy perturbation method are the same and with hexapole and octopole superpositions, the results of this paper are much more closer to the exact results compared with the results of the homotopy perturbation method.

Integrable multi-component generalization of a modified short pulse equation

NASA Astrophysics Data System (ADS)

Matsuno, Yoshimasa

2016-11-01

We propose a multi-component generalization of the modified short pulse (SP) equation which was derived recently as a reduction of Feng's two-component SP equation. Above all, we address the two-component system in depth. We obtain the Lax pair, an infinite number of conservation laws and multisoliton solutions for the system, demonstrating its integrability. Subsequently, we show that the two-component system exhibits cusp solitons and breathers for which the detailed analysis is performed. Specifically, we explore the interaction process of two cusp solitons and derive the formula for the phase shift. While cusp solitons are singular solutions, smooth breather solutions are shown to exist, provided that the parameters characterizing the solutions satisfy certain conditions. Last, we discuss the relation between the proposed system and existing two-component SP equations.

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Onda, K.; Temkin, A.

1985-01-01

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Collision properties of overtaking supersolitons with small amplitudes

NASA Astrophysics Data System (ADS)

Olivier, C. P.; Verheest, F.; Hereman, W. A.

2018-03-01

The collision properties of overtaking small-amplitude supersolitons are investigated for the fluid model of a plasma consisting of cold ions and two-temperature Boltzmann electrons. A reductive perturbation analysis is performed for compositional parameters near the supercritical composition. A generalized Korteweg-de Vries equation with a quartic nonlinearity is derived, referred to as the modified Gardner equation. Criteria for the existence of small-amplitude supersolitons are derived. The modified Gardner equation is shown to be not completely integrable, implying that supersoliton collisions are inelastic, as confirmed by numerical simulations. These simulations also show that supersolitons may reduce to regular solitons as a result of overtaking collisions.

Calculating the thermodynamic properties of aqueous solutions of alkali metal carboxylates

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.; Zhukova, T. V.

2014-06-01

A modified Robinson-Stokes equation with terms that consider the formation of ionic hydrates and associates is used to describe thermodynamic properties of aqueous solutions of electrolytes. The model is used to describe data on the osmotic coefficients of aqueous solutions of alkali metal carboxylates, and to calculate the mean ionic activity coefficients of salts and excess Gibbs energies. The key contributions from ionic hydration and association to the nonideality of solutions is determined by analyzing the contributions of various factors. Relations that connect the hydration numbers of electrolytes with the parameters of the Pitzer-Mayorga equation and a modified Hückel equation are developed.

A new multiscale model to describe a modified Hall-Petch relation at different scales for nano and micro materials

NASA Astrophysics Data System (ADS)

Fadhil, Sadeem Abbas; Alrawi, Aoday Hashim; Azeez, Jazeel H.; Hassan, Mohsen A.

2018-04-01

In the present work, a multiscale model is presented and used to modify the Hall-Petch relation for different scales from nano to micro. The modified Hall-Petch relation is derived from a multiscale equation that determines the cohesive energy between the atoms and their neighboring grains. This brings with it a new term that was originally ignored even in the atomistic models. The new term makes it easy to combine all other effects to derive one modified equation for the Hall-Petch relation that works for all scales together, without the need to divide the scales into two scales, each scale with a different equation, as it is usually done in other works. Due to that, applying the new relation does not require a previous knowledge of the grain size distribution. This makes the new derived relation more consistent and easier to be applied for all scales. The new relation is used to fit the data for Copper and Nickel and it is applied well for the whole range of grain sizes from nano to micro scales.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

Modeling of a complex, polar system with a modified Soave-Redlich-Kwong equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sturnfield, E.A.; Matherne, J.L.

1988-01-01

It is computationally feasible to use a simple equation of state (like a Redlich-Kwong) to calculate liquid fugacity but the simpler equations work well only for moderately non-ideal systems. More complex equations (like Ghemling-Lui-Prausnitz) predict system behavior more accurately but are much more complicated to use and can require fitting many parameters to data. This paper illustrates success in using a modified Redlich-Kwong to model a complex system including water, hydrogen, sub and supercritical ammonia, and amines. The binary interaction parameter ({Kappa}/sub ij/) of the Soave-Redlich-Kwong equation has been modified to be both asymmetric and temperature dependent. Further, the aimore » constant was determined by fitting vapor pressure data. Predicted model results are compared to literature (example 1) or plant data (examples 2-4) for four systems: 1. The ammonia-water binary over a wide range of pressure and temperature including ammonia above its critical. 2. A multicomponent Vapor-Liquid equilibrium flash tank and condenser containg hydrogen, amonia, water, and other heavier compounds. 3. A multicomponent vapor-liquid equilibrium flash tank containing water, heavier mines, and the amine salts. 4. A Liquid-Liquid-Vapor equilibrium decanter system containing water, ammonia, and an organic chloride.« less

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

Application of the Flory-Huggins theory to the solubility of solids in glyceryl trioleate

USGS Publications Warehouse

Chiou, Cary T.; Manes, Milton

1986-01-01

The conventional thermodynamic deviation for ideal solid–liquid solubilities is modified by substituting the Flory–Huggins model for Raoult's law. A comparison of published data for eleven solides in glyceryl trioleate with the predictions of the conventional and modified equations shows that the significantly higher athermal solubilities from the modified equation are in much better agreement with the experimental data. This suggests that discrepancies between the data and the predictions of the conventional model for ideal systems result from the inappropriate use of Raoult's law for systems with significant solute–solvent size disparity rather than from specific interactions.

Generalized cable equation model for myelinated nerve fiber.

PubMed

Einziger, Pinchas D; Livshitz, Leonid M; Mizrahi, Joseph

2005-10-01

Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

Capillary Rise: Validity of the Dynamic Contact Angle Models.

PubMed

Wu, Pingkeng; Nikolov, Alex D; Wasan, Darsh T

2017-08-15

The classical Lucas-Washburn-Rideal (LWR) equation, using the equilibrium contact angle, predicts a faster capillary rise process than experiments in many cases. The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data. The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data. The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W(0), which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

Reconstruction of the modified discrete Langevin equation from persistent time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czechowski, Zbigniew

The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.

Bispectrum from open inflation

NASA Astrophysics Data System (ADS)

Sugimura, Kazuyuki; Komatsu, Eiichiro

2013-11-01

We calculate the bispectrum of primordial curvature perturbations, ζ, generated during ``open inflation.'' Inflation occurs inside a bubble nucleated via quantum tunneling from the background false vacuum state. Our universe lives inside the bubble, which can be described as a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) universe with negative spatial curvature, undergoing slow-roll inflation. We pay special attention to the issue of an initial state for quantum fluctuations. A ``vacuum state'' defined by a positive-frequency mode in de Sitter space charted by open coordinates is different from the Euclidean vacuum (which is equivalent to the so-called ``Bunch-Davies vacuum'' defined by a positive-frequency mode in de Sitter space charted by flat coordinates). Quantum tunneling (bubble nucleation) then modifies the initial state away from the original Euclidean vacuum. While most of the previous study on modifications of the initial quantum state introduces, by hand, an initial time at which the quantum state is modified as well as the form of the modification, an effective initial time naturally emerges and the form is fixed by quantum tunneling in open inflation models. Therefore, open inflation enables a self-consistent computation of the effect of a modified initial state on the bispectrum. We find a term which goes as langleζk1ζk2ζk3ranglepropto1/k12k34 in the so-called squeezed configurations, k3 << k1 ≈ k2, in agreement with the previous study on modifications of the initial state. The bispectrum in the exact folded limit, e.g., k1 = k2+k3, is also enhanced and remains finite. However, these terms are exponentially suppressed when the wavelength of ζ is smaller than the curvature radius of the universe. The leading-order bispectrum is equal to the usual one from single-field slow-roll inflation; the terms specific for open inflation arise only in the sub-leading order when the wavelength of ζ is smaller than the curvature radius.

From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

NASA Astrophysics Data System (ADS)

Yang, Xiao; Du, Dianlou

2010-08-01

The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

Tibial Bowing and Pseudarthrosis in Neurofibromatosis Type 1

DTIC Science & Technology

2015-01-01

controlling for age and sex was used. However, there were no statistically significant differences between NF1 individuals with and without tibial...Dinorah Friedmann-Morvinski (The Salk Institute) presented a different model of glioblastoma in which tumors were induced from fully differentiated...a driver of Schwann cell tumorigenesis. Induction ofWnt signaling was sufficient to induce a transformed phenotype in human Schwann cells, while

Classical and quantum cosmology with two perfect fluids: stiff matter and radiation

NASA Astrophysics Data System (ADS)

Alvarenga, F. G.; Fracalossi, R.; Freitas, R. C.; Gonçalves, S. V. B.

2017-11-01

In this work the homogeneous and isotropic Universe of Friedmann-Robertson-Walker is studied in the presence of two fluids: stiff matter and radiation described by the Schutz's formalism. We obtain to the classic case the behaviour of the scale factor of the universe. For the quantum case the wave packets are constructed and the wave function of the universe is found.

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

Numerical integration of ordinary differential equations of various orders

NASA Technical Reports Server (NTRS)

Gear, C. W.

1969-01-01

Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced.

Digestibility Is Similar between Commercial Diets That Provide Ingredients with Different Perceived Glycemic Responses and the Inaccuracy of Using the Modified Atwater Calculation to Calculate Metabolizable Energy

PubMed Central

Asaro, Natalie J.; Guevara, Marcial A.; Berendt, Kimberley; Zijlstra, Ruurd; Shoveller, Anna K.

2017-01-01

Dietary starch is required for a dry, extruded kibble; the most common diet type for domesticated felines in North America. However, the amount and source of dietary starch may affect digestibility and metabolism of other macronutrients. The objectives of this study were to evaluate the effects of 3 commercial cat diets on in vivo and in vitro energy and macronutrient digestibility, and to analyze the accuracy of the modified Atwater equation. Dietary treatments differed in their perceived glycemic response (PGR) based on ingredient composition and carbohydrate content (34.1, 29.5, and 23.6% nitrogen-free extract for High, Medium, and LowPGR, respectively). A replicated 3 × 3 Latin square design was used, with 3 diets and 3 periods. In vivo apparent protein, fat, and organic matter digestibility differed among diets, while apparent dry matter digestibility did not. Cats were able to efficiently digest and absorb macronutrients from all diets. Furthermore, the modified Atwater equation underestimated measured metabolizable energy by approximately 12%. Thus, the modified Atwater equation does not accurately determine the metabolizable energy of high quality feline diets. Further research should focus on understanding carbohydrate metabolism in cats, and establishing an equation that accurately predicts the metabolizable energy of feline diets. PMID:29117110

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Symmetry Reductions, Integrability and Solitary Wave Solutions to High-Order Modified Boussinesq Equations with Damping Term

NASA Astrophysics Data System (ADS)

Yan, Zhen-Ya; Xie, Fu-Ding; Zhang, Hong-Qing

2001-07-01

Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of Ablowitz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation. The project supported by National Natural Science Foundation of China under Grant No. 19572022, the National Key Basic Research Development Project Program of China under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119

ODE/IM correspondence for modified B2(1) affine Toda field equation

NASA Astrophysics Data System (ADS)

Ito, Katsushi; Shu, Hongfei

2017-03-01

We study the massive ODE/IM correspondence for modified B2(1) affine Toda field equation. Based on the ψ-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q relations, the T-system and the Y-system, which are shown to be related to those of the A3 /Z2 integrable system. We consider the case that the solution of the linear problem has a monodromy around the origin, which imposes nontrivial boundary conditions for the T-/Y-system. The high-temperature limit of the T- and Y-system and their monodromy dependence are studied numerically.

Analytical evaluation of the trajectories of hypersonic projectiles launched into space

NASA Astrophysics Data System (ADS)

Stutz, John David

An equation of motion has been derived that may be solved using simple analytic functions which describes the motion of a projectile launched from the surface of the Earth into space accounting for both Newtonian gravity and aerodynamic drag. The equation of motion is based upon the Kepler equation of motion differential and variable transformations with the inclusion of a decaying angular momentum driving function and appropriate simplifying assumptions. The new equation of motion is first compared to various numerical and analytical trajectory approximations in a non-rotating Earth reference frame. The Modified Kepler solution is then corrected to include Earth rotation and compared to a rotating Earth simulation. Finally, the modified equation of motion is used to predict the apogee and trajectory of projectiles launched into space by the High Altitude Research Project from 1961 to 1967. The new equation of motion allows for the rapid equalization of projectile trajectories and intercept solutions that may be used to calculate firing solutions to enable ground launched projectiles to intercept or rendezvous with targets in low Earth orbit such as ballistic missiles.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

A rain splash transport equation assimilating field and laboratory measurements

USGS Publications Warehouse

Dunne, T.; Malmon, D.V.; Mudd, S.M.

2010-01-01

Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

Evaluation of 11 equations for determining evaporation for a small lake in the North Central United States

USGS Publications Warehouse

Winter, Thomas C.; Rosenberry, Donald O.; Sturrock, A.M.

1995-01-01

Eleven equations for calculating evaporation were compared with evaporation determined by the energy budget method for Williams Lake, Minnesota. Data were obtained from instruments on a raft, on land near the lake, and at a weather station 60 km south of the lake. The comparisons were based on monthly values for the open-water periods of 5 years, a total of 22 months. A modified DeBruin-Keijman, Priestley-Taylor, and a modified Penman equation resulted in monthly evaporation values that agreed most closely with energy budget values. To use these equations, net radiation, air temperature, wind speed, and relative humidity need to be measured near the lake. In addition, thermal surveys need to be made to determine change in heat stored in the lake. If data from distant climate stations are the only data available, and they include solar radiation, the Jensen-Haise and Makkink equations resulted in monthly evaporation values that agreed reasonably well with energy budget values.

Numerical analysis of soliton solutions of the modified Korteweg-de Vries-sine-Gordon equation

NASA Astrophysics Data System (ADS)

Popov, S. P.

2015-03-01

Multisoliton solutions of the modified Korteweg-de Vries-sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge-Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied.

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

Integral transformation solution of free-space cylindrical vector beams and prediction of modified Bessel-Gaussian vector beams.

PubMed

Li, Chun-Fang

2007-12-15

A unified description of free-space cylindrical vector beams is presented that is an integral transformation solution to the vector Helmholtz equation and the transversality condition. In the paraxial condition, this solution not only includes the known J(1) Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wave equations but also predicts two kinds of vector beam, called a modified Bessel-Gaussian vector beam.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Conceptual design of a high-speed electromagnetic switch for a modified flux-coupling-type SFCL and its application in renewable energy system.

PubMed

Chen, Lei; Chen, Hongkun; Yang, Jun; Shu, Zhengyu; He, Huiwen; Shu, Xin

2016-01-01

The modified flux-coupling-type superconducting fault current (SFCL) is a high-efficient electrical auxiliary device, whose basic function is to suppress the short-circuit current by controlling the magnetic path through a high-speed switch. In this paper, the high-speed switch is based on electromagnetic repulsion mechanism, and its conceptual design is carried out to promote the application of the modified SFCL. Regarding that the switch which is consisting of a mobile copper disc, two fixed opening and closing coils, the computational method for the electromagnetic force is discussed, and also the dynamic mathematical model including circuit equation, magnetic field equation as well as mechanical motion equation is theoretically deduced. According to the mathematical modeling and calculation of characteristic parameters, a feasible design scheme is presented, and the high-speed switch's response time can be less than 0.5 ms. For that the modified SFCL is equipped with this high-speed switch, the SFCL's application in a 10 kV micro-grid system with multiple renewable energy sources are assessed in the MATLAB software. The simulations are well able to affirm the SFCL's performance behaviors.

Neutron stars in a perturbative f(R) gravity model with strong magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheoun, Myung-Ki; Deliduman, Cemsinan; Güngör, Can

2013-10-01

In Kaluza-Klein electromagnetism it is natural to associate modified gravity with strong electromagnetic fields. Hence, in this paper we investigate the combined effects of a strong magnetic field and perturbative f(R) gravity on the structure of neutron stars. The effect of an interior strong magnetic field of about 10{sup 17−18} G on the equation of state is derived in the context of a quantum hadrodynamics (QHD) equation of state (EoS) including effects of the magnetic pressure and energy along with occupied Landau levels. Adopting a random orientation of interior field domains, we solve the modified spherically symmetric hydrostatic equilibrium equationsmore » derived for a gravity model with f(R) = R+αR{sup 2}. Effects of both the finite magnetic field and the modified gravity are detailed for various values of the magnetic field and the perturbation parameter α along with a discussion of their physical implications. We show that there exists a parameter space of the modified gravity and the magnetic field strength, in which even a soft equation of state can accommodate a large ( > 2 M{sub s}un) maximum neutron star mass.« less

Properties of blueshifted light rays in quasispherical Szekeres metrics

NASA Astrophysics Data System (ADS)

Krasiński, Andrzej

2018-03-01

This paper is a follow-up on two previous ones, in which properties of blueshifted rays were investigated in Lemaître-Tolman (L-T) and quasispherical Szekeres (QSS) spacetimes. In the present paper, an axially symmetric QSS deformation is superposed on such a L-T background that was proved, in the first paper, to mimic several properties of gamma-ray bursts. The present model makes z closer to -1 than in the background L-T spacetime, and, as implied by the second paper, strong blueshifts exist in it only along two opposite directions. The QSS region is matched into a Friedmann background. The big bang (BB) function tB(r ), which is constant in the Friedmann region, has a gate-shaped hump in the QSS region. Since a QSS island generates stronger blueshifts than a L-T island, the BB hump can be made lower—then, it is further removed from the observer and implies a smaller observed angular radius of the source. Consequently, more sources can be fitted into the sky—all these facts are confirmed by numerical computations. Null geodesics reaching present observers from different directions relative to the BB hump are numerically calculated. Patterns of redshift across the image of the source and along the rays are displayed.

Evolution and dynamics of a matter creation model

NASA Astrophysics Data System (ADS)

Pan, S.; de Haro, J.; Paliathanasis, A.; Slagter, R. J.

2016-08-01

In a flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, we consider the expansion of the universe powered by the gravitationally induced `adiabatic' matter creation. To demonstrate how matter creation works well with the expanding universe, we have considered a general creation rate and analysed this rate in the framework of dynamical analysis. The dynamical analysis hints the presence of a non-singular universe (without the big bang singularity) with two successive accelerated phases, one at the very early phase of the universe (I.e. inflation), and the other one describes the current accelerating universe, where this early, late accelerated phases are associated with an unstable fixed point (I.e. repeller) and a stable fixed point (attractor), respectively. We have described this phenomena by analytic solutions of the Hubble function and the scale factor of the FLRW universe. Using Jacobi last multiplier method, we have found a Lagrangian for this matter creation rate describing this scenario of the universe. To match with our early physics results, we introduce an equivalent dynamics driven by a single scalar field, discuss the associated observable parameters and compare them with the latest Planck data sets. Finally, introducing the teleparallel modified gravity, we have established an equivalent gravitational theory in the framework of matter creation.

Peculiar velocity measurement in a clumpy universe

NASA Astrophysics Data System (ADS)

Habibi, Farhang; Baghram, Shant; Tavasoli, Saeed

Aims: In this work, we address the issue of peculiar velocity measurement in a perturbed Friedmann universe using the deviations from measured luminosity distances of standard candles from background FRW universe. We want to show and quantify the statement that in intermediate redshifts (0.5 < z < 2), deviations from the background FRW model are not uniquely governed by peculiar velocities. Luminosity distances are modified by gravitational lensing. We also want to indicate the importance of relativistic calculations for peculiar velocity measurement at all redshifts. Methods: For this task, we discuss the relativistic correction on luminosity distance and redshift measurement and show the contribution of each of the corrections as lensing term, peculiar velocity of the source and Sachs-Wolfe effect. Then, we use the SNe Ia sample of Union 2, to investigate the relativistic effects, we consider. Results: We show that, using the conventional peculiar velocity method, that ignores the lensing effect, will result in an overestimate of the measured peculiar velocities at intermediate redshifts. Here, we quantify this effect. We show that at low redshifts the lensing effect is negligible compare to the effect of peculiar velocity. From the observational point of view, we show that the uncertainties on luminosity of the present SNe Ia data prevent us from precise measuring the peculiar velocities even at low redshifts (z < 0.2).

Finding a spherically symmetric cosmology from observations in observational coordinates — advantages and challenges

NASA Astrophysics Data System (ADS)

Araújo, M. E.; Stoeger, W. R.

2011-07-01

One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions — without, for instance, assuming that the universe is almost Friedmann-Lemaître-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lemaître-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate y is null (light-like) and measured down the past light cone of the observer. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution — i.e. our procedure is not restricted to our past light cone — and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. We also compare the two approaches with regard to determining the cosmological constant Λ. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations. Smoothed data functions enable us to include properties that data must have within the model.

Enthalpy-based equation of state for highly porous materials employing modified soft sphere fluid model

NASA Astrophysics Data System (ADS)

Nayak, Bishnupriya; Menon, S. V. G.

2018-01-01

Enthalpy-based equation of state based on a modified soft sphere model for the fluid phase, which includes vaporization and ionization effects, is formulated for highly porous materials. Earlier developments and applications of enthalpy-based approach had not accounted for the fact that shocked states of materials with high porosity (e.g., porosity more than two for Cu) are in the expanded fluid region. We supplement the well known soft sphere model with a generalized Lennard-Jones formula for the zero temperature isotherm, with parameters determined from cohesive energy, specific volume and bulk modulus of the solid at normal condition. Specific heats at constant pressure, ionic and electronic enthalpy parameters and thermal excitation effects are calculated using the modified approach and used in the enthalpy-based equation of state. We also incorporate energy loss from the shock due to expansion of shocked material in calculating porous Hugoniot. Results obtained for Cu, even up to initial porosities ten, show good agreement with experimental data.

Impact of Sequential Ammonia Fiber Expansion (AFEX) Pretreatment and Pelletization on the Moisture Sorption Properties of Corn Stover

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonner, Ian J.; Thompson, David N.; Teymouri, Farzaneh

Combining ammonia fiber expansion (AFEX™) pretreatment with a depot processing facility is a promising option for delivering high-value densified biomass to the emerging bioenergy industry. However, because the pretreatment process results in a high moisture material unsuitable for pelleting or storage (40% wet basis), the biomass must be immediately dried. If AFEX pretreatment results in a material that is difficult to dry, the economics of this already costly operation would be at risk. This work tests the nature of moisture sorption isotherms and thin-layer drying behavior of corn (Zea mays L.) stover at 20°C to 60°C before and after sequentialmore » AFEX pretreatment and pelletization to determine whether any negative impacts to material drying or storage may result from the AFEX process. The equilibrium moisture content to equilibrium relative humidity relationship for each of the materials was determined using dynamic vapor sorption isotherms and modeled with modified Chung-Pfost, modified Halsey, and modified Henderson temperature-dependent models as well as the Double Log Polynomial (DLP), Peleg, and Guggenheim Anderson de Boer (GAB) temperature-independent models. Drying kinetics were quantified under thin-layer laboratory testing and modeled using the Modified Page's equation. Water activity isotherms for non-pelleted biomass were best modeled with the Peleg temperature-independent equation while isotherms for the pelleted biomass were best modeled with the Double Log Polynomial equation. Thin-layer drying results were accurately modeled with the Modified Page's equation. The results of this work indicate that AFEX pretreatment results in drying properties more favorable than or equal to that of raw corn stover, and pellets of superior physical stability in storage.« less

Modified Einstein and Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.

Modified Einstein and Navier–Stokes Equations

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

NASA Technical Reports Server (NTRS)

Kleb, William L.; Wood, William A.; vanLeer, Bram

1999-01-01

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

A Viscoelastic Hybrid Shell Finite Element

NASA Technical Reports Server (NTRS)

Johnson, Arthur

1999-01-01

An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

New holographic dark energy model with constant bulk viscosity in modified f(R,T) gravity theory

NASA Astrophysics Data System (ADS)

Srivastava, Milan; Singh, C. P.

2018-06-01

The aim of this paper is to study new holographic dark energy (HDE) model in modified f(R,T) gravity theory within the framework of a flat Friedmann-Robertson-Walker model with bulk viscous matter content. It is thought that the negative pressure caused by the bulk viscosity can play the role of dark energy component, and drive the accelerating expansion of the universe. This is the motive of this paper to observe such phenomena with bulk viscosity. In the specific model f(R,T)=R+λ T, where R is the Ricci scalar, T the trace of the energy-momentum tensor and λ is a constant, we find the solution for non-viscous and viscous new HDE models. We analyze new HDE model with constant bulk viscosity, ζ =ζ 0= const. to explain the present accelerated expansion of the universe. We classify all possible scenarios (deceleration, acceleration and their transition) with possible positive and negative ranges of λ over the constraint on ζ 0 to analyze the evolution of the universe. We obtain the solutions of scale factor and deceleration parameter, and discuss the evolution of the universe. We observe the future finite-time singularities of type I and III at a finite time under certain constraints on λ . We also investigate the statefinder and Om diagnostics of the viscous new HDE model to discriminate with other existing dark energy models. In late time the viscous new HDE model approaches to Λ CDM model. We also discuss the thermodynamics and entropy of the model and find that it satisfies the second law of thermodynamics.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Modifiable Prostate Cancer Risk Reduction and Early Detection Behaviors in Black Men

ERIC Educational Resources Information Center

Odedina, Folakemi T.; Scrivens, John J., Jr.; Larose-Pierre, Margareth; Emanuel, Frank; Adams, Angela Denise; Dagne, Getachew A.; Pressey, Shannon Alexis; Odedina, Oladapo

2011-01-01

Objective: To explore the personal factors related to modifiable prostate cancer risk-reduction and detection behaviors among black men. Methods: Three thousand four hundred thirty (3430) black men were surveyed and structural equation modeling employed to test study hypotheses. Results: Modifiable prostate cancer risk-reduction behavior was found…

Modified homotopy perturbation method for solving hypersingular integral equations of the first kind.

PubMed

Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z

2016-01-01

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

NASA Technical Reports Server (NTRS)

Amano, R. S.; Goel, P.

1986-01-01

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

Binary Mixture of Perfect Fluid and Dark Energy in Modified Theory of Gravity

NASA Astrophysics Data System (ADS)

Shaikh, A. Y.

2016-07-01

A self consistent system of Plane Symmetric gravitational field and a binary mixture of perfect fluid and dark energy in a modified theory of gravity are considered. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = γρ with γ∈ [0, 1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied.

N =4 supersymmetric mechanics on curved spaces

NASA Astrophysics Data System (ADS)

Kozyrev, Nikolay; Krivonos, Sergey; Lechtenfeld, Olaf; Nersessian, Armen; Sutulin, Anton

2018-04-01

We present N =4 supersymmetric mechanics on n -dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten-Dijkgraaf-Verlinde-Verlinde equations specified by the presence of the manifold's curvature tensor. Solutions of original Witten-Dijkgraaf-Verlinde-Verlinde equations and related prepotentials defining N =4 superconformal mechanics in flat space can be lifted to s o (n )-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgs-oscillator potential. In particular, the sum of n copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Stress-Strain Behavior of Cementitious Materials with Different Sizes

PubMed Central

Zhou, Jikai; Qian, Pingping; Chen, Xudong

2014-01-01

The size dependence of flexural properties of cement mortar and concrete beams is investigated. Bazant's size effect law and modified size effect law by Kim and Eo give a very good fit to the flexural strength of both cement mortar and concrete. As observed in the test results, a strong size effect in flexural strength is found in cement mortar than in concrete. A modification has been suggested to Li's equation for describing the stress-strain curve of cement mortar and concrete by incorporating two different correction factors, the factors contained in the modified equation being established empirically as a function of specimen size. A comparison of the predictions of this equation with test data generated in this study shows good agreement. PMID:24744688

Performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data.

PubMed

Yelland, Lisa N; Salter, Amy B; Ryan, Philip

2011-10-15

Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

Galileon string measure and other modified measure extended objects

NASA Astrophysics Data System (ADS)

Vulfs, T. O.; Guendelman, E. I.

2017-12-01

We show that it is possible to formulate string theory as a “Galileon string theory”. The Galileon field χ enters in the definition of the integration measure in the action. Following the methods of the modified measure string theory, we find that the final equations are again those of the sigma-model. Moreover, the string tension appears again as an additional dynamical degree of freedom. At the same time, the theory satisfies all requirements of the Galileon higher derivative theory at the action level while the equations of motion are still of the second-order. A Galileon symmetry is displayed explicitly in the conformal string worldsheet frame. Also, we define the Galileon gauge transformations. Generalizations to branes with other modified measures are discussed.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mcdonald, G. H.

1978-01-01

High frequency combustion instability problems in a liquid fuel annular combustion chamber are examined. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation in order to analyze the problem of instability. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations.

Exact solutions for STO and (3+1)-dimensional KdV-ZK equations using (G‧/G2) -expansion method

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Ullah, Rahmat; Ahmed, Naveed; Khan, Umar

This article deals with finding some exact solutions of nonlinear fractional differential equations (NLFDEs) by applying a relatively new method known as (G‧/G2) -expansion method. Solutions of space-time fractional Sharma-Tasso-Olever (STO) equation of fractional order and (3+1)-dimensional KdV-Zakharov Kuznetsov (KdV-ZK) equation of fractional order are reckoned to demonstrate the validity of this method. The fractional derivative version of modified Riemann-Liouville, linked with Fractional complex transform is employed to transform fractional differential equations into the corresponding ordinary differential equations.

Formation Flight of Earth Satellites on KAM Tori

DTIC Science & Technology

2007-09-01

satellite formations, involves using the Hill- Clohessy - Wiltshire (HCW) equations, created originally for the Gemini Program [2]. These equations are given...the Perturbed J2-Modified Hill- Clohessy - Wiltshire Equations. MS thesis, The University of Texas at Arlington, 2006. 7. Kaasalainen, M. and J. Binney...107 xvii List of Abbreviations Abbreviation Page KAM Kolmogorov, Arnold and Moser . . . . . . . . . . . . . . . . . 2 HCW Hill- Clohessy

Analysis of Jeans instability of optically thick quantum plasma under the effect of modified Ohms law

NASA Astrophysics Data System (ADS)

Pensia, R. K.; Sutar, D. L.; Sharma, S.

2018-05-01

The Jeans instability of self-gravitating optically thick quantum plasma is reanalyzed in the framework of viscosity, black body radiation and modify ohms law. The usual magnetohydrodynamic (MHD) equation is used for the present configuration with black body radiation, viscosity, electrical resistivity and quantum corrections. A general dispersion relation is obtained with the help of linearized perturbation equations. It is found that the quantum correction has stabilizing effect on the system. The instability of system is discussed for various cases as our interest.

Van der Waals equation of state revisited: importance of the dispersion correction.

PubMed

de Visser, Sam P

2011-04-28

One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.

What initial condition of inflation would suppress the large-scale CMB spectrum?

DOE PAGES

Chen, Pisin; Lin, Yu -Hsiang

2016-01-08

There is an apparent power deficit relative to the Λ CDM prediction of the cosmic microwave background spectrum at large scales, which, though not yet statistically significant, persists from WMAP to Planck data. Proposals that invoke some form of initial condition for the inflation have been made to address this apparent power suppression, albeit with conflicting conclusions. By studying the curvature perturbations of a scalar field in the Friedmann-Lemaître-Robertson-Walker universe parameterized by the equation of state parameter w, we find that the large-scale spectrum at the end of inflation reflects the superhorizon spectrum of the initial state. The large-scale spectrummore » is suppressed if the universe begins with the adiabatic vacuum in a superinflation (w < –1) or positive-pressure (w > 0) era. In the latter case, there is however no causal mechanism to establish the initial adiabatic vacuum. On the other hand, as long as the universe begins with the adiabatic vacuum in an era with –1 < w < 0, even if there exists an intermediate positive-pressure era, the large-scale spectrum would be enhanced rather than suppressed. In conclusion, we further calculate the spectrum of a two-stage inflation model with a two-field potential and show that the result agrees with that obtained from the ad hoc single-field analysis.« less

Cosmological rotating black holes in five-dimensional fake supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nozawa, Masato; Maeda, Kei-ichi; Waseda Research Institute for Science and Engineering, Okubo 3-4-1, Shinjuku, Tokyo 169-8555

2011-01-15

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order 'Killing spinor'more » equation in 'fake supergravity' coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial 'Killing spinor', which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.« less

More on cosmological gravitational waves and their memories

NASA Astrophysics Data System (ADS)

Chu, Yi-Zen

2017-10-01

We extend recent theoretical results on the propagation of linear gravitational waves (GWs), including their associated memories, in spatially flat Friedmann-Lemaître-Robertson-Walker universes, for all spacetime dimensions higher than 3. By specializing to a cosmology driven by a perfect fluid with a constant equation-of-state w, conformal re-scaling, dimension-reduction and Nariai’s ansatz may then be exploited to obtain analytic expressions for the graviton and photon Green’s functions, allowing their causal structure to be elucidated. When 0 < w ≤slant 1 , the gauge-invariant scalar mode admits wave solutions, and like its tensor counterpart, likely contributes to the tidal squeezing and stretching of the space around a GW detector. In addition, scalar GWs in 4D radiation dominated universes—like tensor GWs in 4D matter dominated ones—appear to yield a tail signal that does not decay with increasing spatial distance from the source. We then solve electromagnetism in the same cosmologies, and point out a tail-induced electric memory effect. Finally, in even dimensional Minkowski backgrounds higher than 2, we make a brief but explicit comparison between the linear GW memory generated by point masses scattering off each other on unbound trajectories and the linear Yang-Mills memory generated by color point charges doing the same—and point out how there is a ‘double copy’ relation between the two.

The Rh = ct universe in alternative theories of gravity

NASA Astrophysics Data System (ADS)

Sultana, Joseph; Kazanas, Demosthenes

2017-12-01

The Λ cold dark matter (ΛCDM) model (one comprising of a cosmological constant Λ and cold dark matter) is generally considered the standard model in cosmology. One of the alternatives that has received attention in the last few years is the Rh = ct universe, which provides an age for the Universe similar to that of ΛCDM and whose (vanishing) deceleration parameter is apparently not inconsistent with observations. Like the ΛCDM, the Rh = ct universe is based on a Friedmann-Robertson-Walker cosmology with the total energy density ρ and pressure p of the cosmic fluid satisfying the simple equation of state ρ + 3p = 0, i.e. a vanishing total active gravitational mass. In an earlier paper, we examined the possible sources for the Rh = ct universe within general relativity, and we have shown that it still contains a dark energy component, albeit not in the form of a cosmological constant. The growing interest in gravitational theories, alternative to Einstein's general relativity, in cosmology, is mainly driven by the need for cosmological models that attain a late-time accelerated expansion without the presence of a cosmological constant as in the ΛCDM, and thereby avoiding the problems associated with it. In this paper, we discuss some of these common alternative theories and show that the Rh = ct is also a solution to some of them.

Model Selection with Strong-lensing Systems

NASA Astrophysics Data System (ADS)

Leaf, Kyle; Melia, Fulvio

2018-05-01

In this paper, we use an unprecedentedly large sample (158) of confirmed strong lens systems for model selection, comparing five well studied Friedmann-Robertson-Walker cosmologies: ΛCDM, wCDM (the standard model with a variable dark-energy equation of state), the Rh = ct universe, the (empty) Milne cosmology, and the classical Einstein-de Sitter (matter dominated) universe. We first use these sources to optimize the parameters in the standard model and show that they are consistent with Planck, though the quality of the best fit is not satisfactory. We demonstrate that this is likely due to under-reported errors, or to errors yet to be included in this kind of analysis. We suggest that the missing dispersion may be due to scatter about a pure single isothermal sphere (SIS) model that is often assumed for the mass distribution in these lenses. We then use the Bayes information criterion, with the inclusion of a suggested SIS dispersion, to calculate the relative likelihoods and ranking of these models, showing that Milne and Einstein-de Sitter are completely ruled out, while Rh = ct is preferred over ΛCDM/wCDM with a relative probability of ˜73% versus ˜24%. The recently reported sample of new strong lens candidates by the Dark Energy Survey, if confirmed, may be able to demonstrate which of these two models is favoured over the other at a level exceeding 3σ.

Multicentered black holes with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Chimento, Samuele; Klemm, Dietmar

2014-01-01

We present a recipe that allows us to construct multicentered black holes embedded in an arbitrary Friedmann-Lemaître-Robertson-Walker (FLRW) universe. These solutions are completely determined by a function satisfying the conformal Laplace equation on the spatial slices E3, S3, or H3. Since anti-de Sitter (AdS) space can be written in FLRW coordinates, this includes as a special case multicentered black holes in AdS, in the sense that, far away from the black holes, the energy density and the pressure approach the values given by a negative cosmological constant. We study in some detail the physical properties of the single-centered asymptotically AdS case, which does not coincide with the usual Reissner-Nordström-AdS black hole, but is highly dynamical. In particular, we determine the curvature singularities and trapping horizons of this solution, compute the surface gravity of the trapping horizons, and show that the generalized first law of black hole dynamics proposed by Hayward holds in this case. It turns out that the spurious big bang/big crunch singularities that appear when one writes AdS in FLRW form become real in the presence of these dynamical black holes. This implies that actually only one point of the usual conformal boundary of AdS survives in the solutions that we construct. Finally, a generalization to arbitrary dimension is also presented.

Light refraction in the Swiss-cheese model

NASA Astrophysics Data System (ADS)

Csapó, Adelinda; Bene, Gyula

2012-08-01

We investigate light propagation in the Swiss-cheese model. On both sides of Swiss-cheese sphere surfaces, observers resting in the flat Friedmann-Robertson-Walker (FRW) space and the Schwarzschild space respectively, see the same light ray enclosing different angles with the normal. We examine light refraction at each crossing of the boundary surfaces, showing that the angle of refraction is larger than the angle of incidence for both directions of the light.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silva, J.M. Hoff da; Pereira, S.H., E-mail: hoff@feg.unesp.br, E-mail: shpereira@gmail.com

In this paper we present exact solutions to the so-called Elko spinors for three models of expanding universe, namely the de Sitter, linear and the radiation type evolution. The study was restricted to flat, homogeneous and isotropic Friedmann-Robertson-Walker backgrounds. Starting with an Elko spinor we present the solutions for these cases and compare to the case of Dirac spinors. Besides, an attempt to use Elko spinors as a dark energy candidate in the cosmological context is investigated.

de Sitter geodesics

NASA Astrophysics Data System (ADS)

Cotăescu, Ion I.

2017-12-01

The geodesics on the (1 + 3)-dimensional de Sitter (dS) spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lemaître-Robertson-Walker, de Sitter-Painlevé and static local charts with Cartesian space coordinates. Moreover, it is shown that there exists a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.

Passive Environmental ASW Prediction System (PEAPS)

DTIC Science & Technology

1975-03-01

Because the Frye and Pugh equation [1] for sound speed is dominated by temperature terms and requires relatively few program steps compared with...other speed of sound equations , it was used in the sound speed profile sub- program . The equation was modified to use the approximation ASS ASS AP • ASS AZ...in ppt (parts per thousand). 21 The SSP sub- program converts the input data to MKS units for use in the above equation and then converts the resultant

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Application of the Modified Compaction Material Model to the Analysis of Landmine Detonation in Soil with Various Degrees of Water Saturation

DTIC Science & Technology

2007-01-01

Equation of State R2 – Constant in JWL Equation of State σ – Yield Stress T – Temperature...v – Specific volume w – Constant in JWL Equation of State x – Spatial coordinate y – Spatial coordinate Y – Yield stress Subscripts Comp – Value at...Constant in JWL Equation of State α – Porosity B – Compaction Modulus B1 – Strain Hardening Constant B2 – Constant in JWL Equation of State

Symmetry Reductions of Fourth-Order Nonlinear Diffusion Equations: Lubrication Model and Some Generalizations

NASA Astrophysics Data System (ADS)

Gandarias, M. L.; Medina, E.

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation ut = (unuxxxx)x or the corresponding modified version ut = unuxxxx play an important role in the study of the interface movements. In this work we analyze the generalizations of the above equations given by ut = (f(u)uxxxx)x, ut = (f(u)uxxxx, and we find that if f(u) = un or f(u) = e-u the equations admit extra classical symmetries. The corresponding reductions are performed and some solutions are characterized.

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Sun, Yan

2018-01-01

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.

PubMed

Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya

2015-07-01

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Elementary Hemodynamic Principles Based on Modified Bernoulli's Equation.

ERIC Educational Resources Information Center

Badeer, Henry S.

1985-01-01

Develops and expands basic concepts of Bernoulli's equation as it applies to vascular hemodynamics. Simple models are used to illustrate gravitational potential energy, steady nonturbulent flow, pump-driven streamline flow, and other areas. Relationships to the circulatory system are also discussed. (DH)

Modeling electrokinetics in ionic liquids: General

DOE PAGES

Wang, Chao; Bao, Jie; Pan, Wenxiao; ...

2017-04-01

Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson–Nernst–Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson-Nernst-Planck equations are coupled with Navier–Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double-layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion-selective surface, and electroconvective flow on amore » curved ionselective surface. Lastly, we also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.« less

Quantitative assessment of corneal viscoelasticity using optical coherence elastography and a modified Rayleigh-Lamb equation

NASA Astrophysics Data System (ADS)

Han, Zhaolong; Aglyamov, Salavat R.; Li, Jiasong; Singh, Manmohan; Wang, Shang; Vantipalli, Srilatha; Wu, Chen; Liu, Chih-hao; Twa, Michael D.; Larin, Kirill V.

2015-02-01

We demonstrate the use of a modified Rayleigh-Lamb frequency equation in conjunction with noncontact optical coherence elastography to quantify the viscoelastic properties of the cornea. Phase velocities of air-pulse-induced elastic waves were extracted by spectral analysis and used for calculating the Young's moduli of the samples using the Rayleigh-Lamb frequency equation (RLFE). Validation experiments were performed on 2% agar phantoms (n=3) and then applied to porcine corneas (n=3) in situ. The Young's moduli of the porcine corneas were estimated to be ˜60 kPa with a shear viscosity ˜0.33 Pa.s. The results demonstrate that the RLFE is a promising method for noninvasive quantification of the corneal biomechanical properties and may potentially be useful for clinical ophthalmological applications.

Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

2018-05-01

We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

Relativistic effects due to gravimagnetic moment of a rotating body

NASA Astrophysics Data System (ADS)

Ramírez, Walberto Guzmán; Deriglazov, Alexei A.

2017-12-01

We compute the exact Hamiltonian (and corresponding Dirac brackets) for a spinning particle with gravimagnetic moment κ in an arbitrary gravitational background. The case κ =0 corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. κ =1 leads to modified MPTD equations with improved behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. The rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with the MPTD body: (A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. (B) For specific binary systems, gravimagnetic moment gives a contribution to the frame-dragging effect with the magnitude that turns out to be comparable with that of Schiff frame dragging.

Composite anion-exchangers modified with nanoparticles of hydrated oxides of multivalent metals

NASA Astrophysics Data System (ADS)

Maltseva, T. V.; Kolomiets, E. O.; Dzyazko, Yu. S.; Scherbakov, S.

2018-02-01

Organic-inorganic composite ion-exchangers based on anion exchange resins have been obtained. Particles of one-component and two-component modifier were embedded using the approach, which allows us to realize purposeful control of a size of the embedded particles. The approach is based on Ostwald-Freundlich equation, which was adapted to deposition in ion exchange matrix. The equation was obtained experimentally. Hydrated oxides of zirconium and iron were applied to modification, concentration of the reagents were varied. The embedded particles accelerate sorption, the rate of which is fitted by the model equation of chemical reactions of pseudo-second order. When sorption of arsenate ions from very diluted solution (50 µg dm-3) occurs, the composites show higher distribution coefficients comparing with the pristine resin.

Modified QCD ghost f(T,TG) gravity

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Rani, Shamaila; Chattopadhyay, Surajit

2015-12-01

In this paper, we explore the reconstruction scenario of modified QCD ghost dark energy model and newly proposed f(T,TG) gravity in flat FRW universe. We consider the well-known assumption of scale factor, i.e., power law form. We construct the f(T,TG) model and discuss its cosmological consequences through various cosmological parameters such as equation of state parameter, squared speed of sound and ω_{DE}-ω '_{DE}. The equation of state parameter provides the quintom-like behavior of the universe. The squared speed of sound exhibits the stability of model in the later time. Also, ω_{DE}- ω '_{DE} corresponds to freezing as well as thawing regions. It is also interesting to remark here that the results of equation of state parameter and w_{DE}-w'_{DE} coincide with the observational data.

Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses.

PubMed

Cabrales, Luis E Bergues; Nava, Juan J Godina; Aguilera, Andrés Ramírez; Joa, Javier A González; Ciria, Héctor M Camué; González, Maraelys Morales; Salas, Miriam Fariñas; Jarque, Manuel Verdecia; González, Tamara Rubio; Mateus, Miguel A O'Farril; Brooks, Soraida C Acosta; Palencia, Fabiola Suárez; Zamora, Lisset Ortiz; Quevedo, María C Céspedes; Seringe, Sarah Edward; Cuitié, Vladimir Crombet; Cabrales, Idelisa Bergues; González, Gustavo Sierra

2010-10-28

Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.

Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations

NASA Astrophysics Data System (ADS)

Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, A. A.

2016-02-01

We consider the ABF background underlying the η-deformed AdS5 ×S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R-R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R-R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3 ×S3 ×T4and AdS2 ×S2 ×T6models.

Scale invariance of the η-deformed AdS 5 × S 5 superstring, T-duality and modified type II equations

DOE PAGES

Arutyunov, G.; Frolov, S.; Hoare, B.; ...

2015-12-23

We consider the ABF background underlying the η-deformed AdS 5 × S 5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that hasmore » 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R–R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R–R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS 3 × S 3 × T 4 and AdS 2 × S 2 × T 6 models.« less

Modeling the Nonlinear, Strain Rate Dependent Deformation of Shuttle Leading Edge Materials with Hydrostatic Stress Effects Included

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Carney, Kelly S.

2004-01-01

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites, such as the Reinforced Carbon Carbon (RCC) material used on the leading edges of the Space Shuttle. In the developed model, the differences in the tension and compression deformation behaviors have also been accounted for. State variable viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear response is independent of the stiffness in the normal directions. The developed equations have been implemented into LS-DYNA through the use of user defined subroutines (UMATs). Several sample qualitative calculations have been conducted, which demonstrate the ability of the model to qualitatively capture the features of the deformation response present in woven ceramic matrix composites.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

Numeric Modified Adomian Decomposition Method for Power System Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth

This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested.more » It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.« less

CRE Solvability, Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation

NASA Astrophysics Data System (ADS)

Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo

2017-06-01

This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009

An energy-stable method for solving the incompressible Navier-Stokes equations with non-slip boundary condition

NASA Astrophysics Data System (ADS)

Lee, Byungjoon; Min, Chohong

2018-05-01

We introduce a stable method for solving the incompressible Navier-Stokes equations with variable density and viscosity. Our method is stable in the sense that it does not increase the total energy of dynamics that is the sum of kinetic energy and potential energy. Instead of velocity, a new state variable is taken so that the kinetic energy is formulated by the L2 norm of the new variable. Navier-Stokes equations are rephrased with respect to the new variable, and a stable time discretization for the rephrased equations is presented. Taking into consideration the incompressibility in the Marker-And-Cell (MAC) grid, we present a modified Lax-Friedrich method that is L2 stable. Utilizing the discrete integration-by-parts in MAC grid and the modified Lax-Friedrich method, the time discretization is fully discretized. An explicit CFL condition for the stability of the full discretization is given and mathematically proved.

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

PubMed

Suárez, G; Hoyuelos, M; Mártin, H

2016-06-01

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1999-01-01

An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chamseddine, Ali H.; Mukhanov, Viatcheslav, E-mail: chams@aub.edu.lb, E-mail: viatcheslav.mukhanov@physik.uni-muenchen.de

We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the universe has a regular bounce which takes place during the time inversely proportional to the square root of the limiting curvature. Away from the bounce, corrections to General Relativity are negligible. In addition the non-singluar modification of General Relativity delivers for free a realistic candidate for Dark Matter.

Neutrinos and the age of the universe

NASA Technical Reports Server (NTRS)

Symbalisty, E. M. D.; Yang, J.; Schramm, D. N.

1980-01-01

The age of the universe should be calculable by independent methods with similar results. Previous calculations using nucleochronometers, globular clusters and dynamical measurements coupled with Friedmann models and nucleosynthesis constraints have given different values of the age. A consistent age is reported, whose implications for the constituent mass density are very interesting and are affected by the existence of a third neutrino flavor, and by allowing the possibility that neutrinos may have a non-zero rest mass.

Some dynamical aspects of interacting quintessence model

NASA Astrophysics Data System (ADS)

Choudhury, Binayak S.; Mondal, Himadri Shekhar; Chatterjee, Devosmita

2018-04-01

In this paper, we consider a particular form of coupling, namely B=σ (\\dot{ρ _m}-\\dot{ρ _φ }) in spatially flat (k=0) Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time. We perform phase-space analysis for this interacting quintessence (dark energy) and dark matter model for different numerical values of parameters. We also show the phase-space analysis for the `best-fit Universe' or concordance model. In our analysis, we observe the existence of late-time scaling attractors.

Higher dimensional strange quark matter solutions in self creation cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Şen, R., E-mail: ramazansen-1991@hotmail.com; Aygün, S., E-mail: saygun@comu.edu.tr

In this study, we have generalized the higher dimensional flat Friedmann-Robertson-Walker (FRW) universe solutions for a cloud of string with perfect fluid attached strange quark matter (SQM) in Self Creation Cosmology (SCC). We have obtained that the cloud of string with perfect fluid does not survive and the string tension density vanishes for this model. However, we get dark energy model for strange quark matter with positive density and negative pressure in self creation cosmology.

The tethered galaxy problem: a possible window to explore cosmological models

NASA Astrophysics Data System (ADS)

Tangmatitham, Matipon; Nemiroff, Robert J.

2017-01-01

In the tethered galaxy problem, a hypothetical galaxy is being held at a fixed proper distance. Contrary to Newtonian intuition, it has been shown that this tethered galaxy can have a nonzero redshift. However, constant proper distance has been suggested as unphysical in a cosmological setting and therefore other definitions have been suggested. The tethered galaxy problem is therefore reviewed in Friedmann cosmology. In this work, different tethers are considered as possible local cosmological discriminators.

Coal without carbon: an investment plan for federal action

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pettus, A.; Tatsutani, M.

2009-09-15

This study examines several technologies for CCS that are not currently receiving adequate development support but that could - in the right policy environment - provide the kind of significant cost reductions (and significant improvements in efficiency) that could greatly accelerate broad, economically attractive CCS deployment. Clean Air Task Force selected these technology areas (though not the technologies themselves) and solicited reports from experts in each field to explore how these technologies might fit into a broader CCS deployment strategy. Each expert was asked to develop a research, development, and demonstration (RD&D) 'road map' that could efficiently move each technologymore » from the laboratory into the commercial mainstream. Because the chapter authors are either technical experts or commercial players and are not, for the most part, energy policy experts, subsequent work will translate their RD&D recommendations into actionable policy proposals. The heart of this report consists of four chapters on advanced coal and CCS technologies: underground coal gasification (UCG), written by Julio Friedmann at Lawrence Livermore National Laboratory; Next generation coal gasification (surface-based gasification) led by Eric Redman at Summit Power Group; Advanced technologies for post-combustion capture (PCC) of CO{sub 2}, led by Howard Herzog at Massachusetts Institute of Technology; and RD&D to speed commercialization of geological CO{sub 2} sequestration (GCS), led by Julio Friedmann. 12 refs., 5 figs., 2 tabs.« less

Non-Friedmann cosmology for the Local Universe, significance of the universal Hubble constant, and short-distance indicators of dark energy

NASA Astrophysics Data System (ADS)

Chernin, A. D.; Teerikorpi, P.; Baryshev, Yu. V.

2006-09-01

Based on the increasing evidence of the cosmological relevance of the local Hubble flow, we consider a simple analytical cosmological model for the Local Universe. This is a non-Friedmann model with a non-uniform static space-time. The major dynamical factor controlling the local expansion is the antigravity produced by the omnipresent and permanent dark energy of the cosmic vacuum (or the cosmological constant). The antigravity dominates at larger distances than 1-2 Mpc from the center of the Local group. The model gives a natural explanation of the two key quantitative characteristics of the local expansion flow, which are the local Hubble constant and the velocity dispersion of the flow. The observed kinematical similarity of the local and global flows of expansion is clarified by the model. We analytically demonstrate the efficiency of the vacuum cooling mechanism that allows one to see the Hubble law this close to the Local group. The "universal Hubble constant" HV (≈60 km s-1 Mpc-1), depending only on the vacuum density, has special significance locally and globally. The model makes a number of verifiable predictions. It also unexpectedly shows that the dwarf galaxies of the local flow with the shortest distances and lowest redshifts may be the most sensitive indicators of dark energy in our neighborhood.

Electrodynamics in the Friedmann Robertson Walker universe: Maxwell and Dirac fields in Newman Penrose formalism

NASA Astrophysics Data System (ADS)

Khanal, U.

2006-07-01

Maxwell and Dirac fields in Friedmann Robertson Walker (FRW) spacetime are investigated using the Newman Penrose method. The variables are all separable, with the angular dependence given by spin-weighted spherical harmonics. All the radial parts reduce to the barrier penetration problem, with mostly repulsive potentials representing the centrifugal energies. Both the helicity states of the photon field see the same potential, but that of the Dirac field see different ones; one component even sees attractive potential in the open universe. The massless fields have the usual exponential time dependences; that of the massive Dirac field is coupled to the evolution of the cosmic scale factor a. The case of the radiation-filled flat universe is solved in terms of the Whittaker function. A formal series solution, valid in any FRW universe, is also presented. The energy density of the Maxwell field is explicitly shown to scale as a-4. The co-moving particle number density of the massless Dirac field is found to be conserved, but that of the massive one is not. Particles flow out of certain regions, and into others, creating regions that are depleted of certain linear and angular momenta states, and others with excess. Such a current of charged particles would constitute an electric current that could generate a cosmic magnetic field. In contrast, the energy density of these massive particles still scales as a-4.

There was movement that was stationary, for the four-velocity had passed around

NASA Astrophysics Data System (ADS)

Roukema, Boudewijn F.

2010-05-01

Is the Doppler interpretation of galaxy redshifts in a Friedmann-Lemaître-Robertson-Walker (FLRW) model valid in the context of the approach to comoving spatial sections pioneered by de Sitter, Friedmann, Lemaître and Robertson, i.e. according to which the three-manifold of comoving space is characterized by both its curvature and topology? Holonomy transformations for flat, spherical and hyperbolic FLRW spatial sections are proposed. By quotienting a simply connected FLRW spatial section by an appropriate group of holonomy transformations, the Doppler interpretation in a non-expanding Minkowski space-time, obtained via four-velocity parallel transport along a photon path, is found to imply that an inertial observer is receding from herself at a speed greater than zero, implying contradictory world lines. The contradiction in the multiply connected case occurs for arbitrary redshifts in the flat and spherical cases, and for certain large redshifts in the hyperbolic case. The link between the Doppler interpretation of redshifts and cosmic topology can be understood physically as the link between parallel transport along a photon path and the fact that the comoving spatial geodesic corresponding to a photon's path can be a closed loop in an FLRW model of any curvature. Closed comoving spatial loops are fundamental to cosmic topology. With apologies to Andrew Barton `Banjo' Paterson. E-mail: boud@astro.uni.torun.pl

Axial quasinormal modes of static neutron stars in the nonminimal derivative coupling sector of Horndeski gravity: Spectrum and universal relations for realistic equations of state

NASA Astrophysics Data System (ADS)

Blázquez-Salcedo, Jose Luis; Eickhoff, Kevin

2018-05-01

We study axial quasinormal modes of static neutron stars in the nonminimal derivative coupling sector of Horndeski theory. We focus on the fundamental curvature mode, which we analyze for 10 different equations of state with different matter content. A comparison with the results obtained in pure general relativity reveals that, apart from modifying the spectrum of the frequencies and the damping times of the stars, this theory modifies several universal relations between the modes and physical parameters of the stars that are otherwise matter independent.

Bending of solitons in weak and slowly varying inhomogeneous plasma

NASA Astrophysics Data System (ADS)

Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan

2015-12-01

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Bending of solitons in weak and slowly varying inhomogeneous plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-12-15

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Ordinary Differential Equation Models for Adoptive Immunotherapy.

PubMed

Talkington, Anne; Dantoin, Claudia; Durrett, Rick

2018-05-01

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Membrane paradigm of black holes in Chern-Simons modified gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Tian-Yi; Wang, Towe, E-mail: zhaotianyi5566@foxmail.com, E-mail: twang@phy.ecnu.edu.cn

2016-06-01

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.

Superstatistics of the Klein-Gordon equation in deformed formalism for modified Dirac delta distribution

NASA Astrophysics Data System (ADS)

Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-04-01

The Klein-Gordon equation is extended in the presence of an Aharonov-Bohm magnetic field for the Cornell potential and the corresponding wave functions as well as the spectra are obtained. After introducing the superstatistics in the statistical mechanics, we first derived the effective Boltzmann factor in the deformed formalism with modified Dirac delta distribution. We then use the concepts of the superstatistics to calculate the thermodynamics properties of the system. The well-known results are recovered by the vanishing of deformation parameter and some graphs are plotted for the clarity of our results.

HST3D; a computer code for simulation of heat and solute transport in three-dimensional ground-water flow systems

USGS Publications Warehouse

Kipp, K.L.

1987-01-01

The Heat- and Soil-Transport Program (HST3D) simulates groundwater flow and associated heat and solute transport in three dimensions. The three governing equations are coupled through the interstitial pore velocity, the dependence of the fluid density on pressure, temperature, the solute-mass fraction , and the dependence of the fluid viscosity on temperature and solute-mass fraction. The solute transport equation is for only a single, solute species with possible linear equilibrium sorption and linear decay. Finite difference techniques are used to discretize the governing equations using a point-distributed grid. The flow-, heat- and solute-transport equations are solved , in turn, after a particle Gauss-reduction scheme is used to modify them. The modified equations are more tightly coupled and have better stability for the numerical solutions. The basic source-sink term represents wells. A complex well flow model may be used to simulate specified flow rate and pressure conditions at the land surface or within the aquifer, with or without pressure and flow rate constraints. Boundary condition types offered include specified value, specified flux, leakage, heat conduction, and approximate free surface, and two types of aquifer influence functions. All boundary conditions can be functions of time. Two techniques are available for solution of the finite difference matrix equations. One technique is a direct-elimination solver, using equations reordered by alternating diagonal planes. The other technique is an iterative solver, using two-line successive over-relaxation. A restart option is available for storing intermediate results and restarting the simulation at an intermediate time with modified boundary conditions. This feature also can be used as protection against computer system failure. Data input and output may be in metric (SI) units or inch-pound units. Output may include tables of dependent variables and parameters, zoned-contour maps, and plots of the dependent variables versus time. (Lantz-PTT)

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

2017-11-01

Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

Modification process optimization, characterization and adsorption property of granular fir-based activated carbon

NASA Astrophysics Data System (ADS)

Chen, Congjin; Li, Xin; Tong, Zhangfa; Li, Yue; Li, Mingfei

2014-10-01

Granular fir-based activated carbon (GFAC) was modified with H2O2, and orthogonal array experimental design method was used to optimize the process. The properties of the original and modified GFAC were characterized by N2 adsorption-desorption isotherms, Brunauer-Emmett-Teller (BET) equation, Barett-Joyner-Halenda (BJH) equation, field emission scanning electron microscopy (FESEM), and Fourier transform infrared spectroscopy (FT-IR) analysis, etc. When 10.00 g of GFAC with particle size of 0.25-0.85 mm was modified by 150.0 ml of aqueous H2O2 solution, the optimized conditions were found to be as follows: aqueous H2O2 solution concentration 1.0 mol·l-1, modification temperature 30.0 °C, modification time 4.0 h. Modified under the optimized conditions, decolonization of caramel, methylene blue adsorption, phenol adsorption and iodine number of the modified GFAC increased by 500.0%, 59.7%, 32.5%, and 15.1%, respectively. The original and optimally modified GFAC exhibited adsorption isotherms of hybrid Type I-IV isotherms with H4 hysteresis. BET surface area, micropore area, total pore volume, micropore volume, and microporosity of the modified GFAC increased by 7.33%, 11.25%, 3.89%, 14.23%, 9.91%, respectively. Whereas the average pore width decreased by 3.16%. In addition, the amount of surface oxygen groups (such as carbonyl or carboxyl) increased in the modified GFAC.

Enthalpy measurement of coal-derived liquids. Final report, April 1981-September 1983. [517 to 10342 kPa; 340 to 664 K

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kidnay, A.J.; Yesavage, V.F.

This report summarizes the results of experimental measurements of enthalpies for quinoline using a freon boil-off flow calorimeter, and an investigation of the applicability of cubic equations of state to correlating the enthalpy of coal-liquids. In Part A the compound quinoline is discussed. Process flow in the flow calorimeter, operational problems, and equipment modifications are described. Procedural modifications, including a new sample purification procedure, are described. Part B discusses the correlational effort. This includes a discussion of past correlational work and the difficulties associated with a general correlation for coal liquid enthalpy. In addition experimental data and computer generated predictionsmore » are presented. Three equations of state were used to predict vapor pressures and enthalpies for ten pure component systems previously studied in the lab. In general, the results were encouraging. All three equations were found to be effective in predicting both enthalpies and vapor pressures. In addition, the equations worked well when fit to mixture enthalpies. The Modified SRK equation was found to be superior to the other equations and modeled all properties for both associating and nonassociating systems well. The Modified SRK equation did have a drawback in that it was not readily generalized since it required two parameters which must be fit to data for best results. In sum, it was shown that a four parameter equation of state could be used successfully to correlate the enthalpy of coal-liquid model compounds.« less

Modified Maturity Offset Prediction Equations: Validation in Independent Longitudinal Samples of Boys and Girls.

PubMed

Kozieł, Sławomir M; Malina, Robert M

2018-01-01

Predicted maturity offset and age at peak height velocity are increasingly used with youth athletes, although validation studies of the equations indicated major limitations. The equations have since been modified and simplified. The objective of this study was to validate the new maturity offset prediction equations in independent longitudinal samples of boys and girls. Two new equations for boys with chronological age and sitting height and chronological age and stature as predictors, and one equation for girls with chronological age and stature as predictors were evaluated in serial data from the Wrocław Growth Study, 193 boys (aged 8-18 years) and 198 girls (aged 8-16 years). Observed age at peak height velocity for each youth was estimated with the Preece-Baines Model 1. The original prediction equations were included for comparison. Predicted age at peak height velocity was the difference between chronological age at prediction and maturity offset. Predicted ages at peak height velocity with the new equations approximated observed ages at peak height velocity in average maturing boys near the time of peak height velocity; a corresponding window for average maturing girls was not apparent. Compared with observed age at peak height velocity, predicted ages at peak height velocity with the new and original equations were consistently later in early maturing youth and earlier in late maturing youth of both sexes. Predicted ages at peak height velocity with the new equations had reduced variation compared with the original equations and especially observed ages at peak height velocity. Intra-individual variation in predicted ages at peak height velocity with all equations was considerable. The new equations are useful for average maturing boys close to the time of peak height velocity; there does not appear to be a clear window for average maturing girls. The new and original equations have major limitations with early and late maturing boys and girls.

Twin Paradox: A Complete Treatment from the Point of View of Each Twin.

ERIC Educational Resources Information Center

Perrin, Robert

1979-01-01

Modifies and expands on the treatment of the twin paradox by solving the gravitational field equations and geodesic equations of motion in the traveling twin's reference frame, thus determining the time elapsed on the Earth during the periods of acceleration. (Author/GA)

Regression Simulation Model. Appendix X. Users Manual,

DTIC Science & Technology

1981-03-01

change as the prediction equations become refined. Whereas no notice will be provided when the changes are made, the programs will be modified such that...NATIONAL BUREAU Of STANDARDS 1963 A ___,_ __ _ __ _ . APPENDIX X ( R4/ EGRESSION IMULATION ’jDEL. Ape’A ’) 7 USERS MANUA submitted to The Great River...regression analysis and to establish a prediction equation (model). The prediction equation contains the partial regression coefficients (B-weights) which

Anticancer Agents Based on a New Class of Transition- State Analog Inhibitors for Serine and Cysteine Proteases

DTIC Science & Technology

1999-08-01

electrostatic repulsion between the het- eroatom and the ketone. Swain and Lupton31 have constructed a modified Hammett equation (eq 2) in which they...determined by nonlinear fit to the Michaelis-Menten equation for competitive inhibition using simple weighing. Competitive inhibition was confirmed... equation for competitive inhibition using simple weighing. Competitive inhibition was confirmed by Lineweaver - Burk analysis using simple

Rogue periodic waves of the modified KdV equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

A modified exponential behavioral economic demand model to better describe consumption data.

PubMed

Koffarnus, Mikhail N; Franck, Christopher T; Stein, Jeffrey S; Bickel, Warren K

2015-12-01

Behavioral economic demand analyses that quantify the relationship between the consumption of a commodity and its price have proven useful in studying the reinforcing efficacy of many commodities, including drugs of abuse. An exponential equation proposed by Hursh and Silberberg (2008) has proven useful in quantifying the dissociable components of demand intensity and demand elasticity, but is limited as an analysis technique by the inability to correctly analyze consumption values of zero. We examined an exponentiated version of this equation that retains all the beneficial features of the original Hursh and Silberberg equation, but can accommodate consumption values of zero and improves its fit to the data. In Experiment 1, we compared the modified equation with the unmodified equation under different treatments of zero values in cigarette consumption data collected online from 272 participants. We found that the unmodified equation produces different results depending on how zeros are treated, while the exponentiated version incorporates zeros into the analysis, accounts for more variance, and is better able to estimate actual unconstrained consumption as reported by participants. In Experiment 2, we simulated 1,000 datasets with demand parameters known a priori and compared the equation fits. Results indicated that the exponentiated equation was better able to replicate the true values from which the test data were simulated. We conclude that an exponentiated version of the Hursh and Silberberg equation provides better fits to the data, is able to fit all consumption values including zero, and more accurately produces true parameter values. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

PubMed

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

aLicante sUrgical Community Emergencies New Tool for the enUmeration of Morbidities: a simplified auditing tool for community-acquired gastrointestinal surgical emergencies.

PubMed

Villodre, Celia; Rebasa, Pere; Estrada, José Luís; Zaragoza, Carmen; Zapater, Pedro; Mena, Luís; Lluís, Félix

2016-11-01

In a previous study, we found that Physiological and Operative Severity Score for the enUmeration of Mortality and Morbidity (POSSUM) overpredicts morbidity risk in emergency gastrointestinal surgery. Our aim was to find a POSSUM equation adjustment. A prospective observational study was performed on 2,361 patients presenting with a community-acquired gastrointestinal surgical emergency. The first 1,000 surgeries constituted the development cohort, the second 1,000 events were the first validation intramural cohort, and the remaining 361 cases belonged to a second validation extramural cohort. (1) A modified POSSUM equation was obtained. (2) Logistic regression was used to yield a statistically significant equation that included age, hemoglobin, white cell count, sodium and operative severity. (3) A chi-square automatic interaction detector decision tree analysis yielded a statistically significant equation with 4 variables, namely cardiac failure, sodium, operative severity, and peritoneal soiling. A modified POSSUM equation and a simplified scoring system (aLicante sUrgical Community Emergencies New Tool for the enUmeration of Morbidities [LUCENTUM]) are described. Both tools significantly improve prediction of surgical morbidity in community-acquired gastrointestinal surgical emergencies. Copyright © 2016 Elsevier Inc. All rights reserved.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Some exact solutions of (2+1)-dimensional Yang-Mills equations with the Chern-Simons term

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oh, C. H.; Sia, L. C.; Teh, R.

1989-07-15

Two /ital Ansa/$/ital uml/---/ital tze/ for the gauge field potential are given so that the(2+1)-dimensional Yang-Mills equations with the Chern-Simons termcan be solved in terms of the modified Bessel functions and the ellipticfunction respectively.