scholarly journals On f(R) Theories in Two-Dimensional Spacetime

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
M. A. Ahmed
Keyword(s):  
Exact Solutions ◽  
Ricci Scalar ◽  
Two Dimensional ◽  
Field Equations ◽  
Dimensional Spacetime ◽  
Set Up

In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function f(R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this paper we carry out an analysis of such theories in two-dimensional spacetime with focus on cosmological implications. Solutions to the cosmological field equations are obtained and their properties are analysed. Inflationary solutions are also obtained and discussed. Quantization is then carried out, the Wheeler-DeWitt equation is set up, and its exact solutions are obtained.

ON TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (37) ◽  
pp. 3521-3526
Author(s):  
S.K. BOSE
Keyword(s):  
Two Dimensions ◽  
Ricci Scalar ◽  
Two Dimensional ◽  
Field Equations ◽  
Existence Of A Solution ◽  
Static Vacuum ◽  
Gravitational Action ◽  
Vacuum Metrics ◽  
Dimensional Gravity

The field equations that result from the use of R2–the square of the Ricci scalar – in the gravitational action are studied in two dimensions. Some general features of the model are noted; in particular, the existence of a solution R=Λ. The form of the static vacuum metrics is obtained. The problem of cosmology is discussed.

scholarly journals Exact solutions of three-dimensional black holes: Einstein gravity versus F(R) gravity

2014 ◽  
Vol 23 (11) ◽  
pp. 1450088 ◽  
Author(s):  
S. H. Hendi ◽  
B. Eslam Panah ◽  
R. Saffari
Keyword(s):  
Black Hole ◽  
Exact Solutions ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Nonlinear Electrodynamics ◽  
Thermodynamic Quantities ◽  
Field Equations ◽  
First Law Of Thermodynamics ◽  
Conformally Invariant ◽  
Dimensional Spacetime

In this paper, we consider Einstein gravity in the presence of a class of nonlinear electrodynamics, called power Maxwell invariant (PMI). We take into account (2 + 1)-dimensional spacetime in Einstein-PMI gravity and obtain its black hole solutions. Then, we regard pure F(R) gravity as well as F(R)-conformally invariant Maxwell (CIM) theory to obtain exact solutions of the field equations with black hole interpretation. Finally, we investigate the conserved and thermodynamic quantities and discuss about the first law of thermodynamics for the mentioned gravitational models.

SOLUTIONS FOR THE SU(2) CHIRAL FIELD EQUATIONS WITHOUT SPATIAL SYMMETRY

1989 ◽  
Vol 04 (20) ◽  
pp. 1915-1922
Author(s):  
HANS J. WOSPAKRIK
Keyword(s):  
Harmonic Function ◽  
Exact Solutions ◽  
Harmonic Mappings ◽  
Chiral Field ◽  
Field Equations ◽  
Spatial Symmetry ◽  
Affine Parameter ◽  
Dimensional Spacetime

Some exact solutions for the SU(2) chiral field equations in the Euclidean and Minkowskian four dimensional spacetime without spatial symmetry are presented. This is achieved by using the harmonic mappings method. Precisely, these solutions correspond to the geodesics of the 3-sphere S3, where the affine parameter is a harmonic function of spacetime.

scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

scholarly journals Some nozzle flows found by the hodograph method

1959 ◽  
Vol 1 (1) ◽  
pp. 80-94 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Exact Solutions ◽  
Two Dimensions ◽  
Nozzle Design ◽  
Perfect Gas ◽  
Field Equations ◽  
Rigid Boundary ◽  
Hodograph Method ◽  
Isentropic Flow ◽  
Fixed Boundaries ◽  
Nozzle Flows

For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.

Comparative studies of the set up of two-dimensional pneumatic arm systems by muscle and rotational actuators

2007 ◽  
Vol 221 (5) ◽  
pp. 743-748 ◽  
Author(s):  
Y-T Wang ◽  
R-H Wong ◽  
J-T Lu
Keyword(s):  
Control Systems ◽  
Fuzzy Controller ◽  
Control Algorithms ◽  
Two Dimensional ◽  
Pneumatic Control ◽  
Learning Mechanism ◽  
Set Up ◽  
And Control ◽  
Self Learning ◽  
System Characteristics

As opposed to traditional pneumatic linear actuators, muscle and rotational actuators are newly developed actuators in rotational and specified applications. In the current paper, these actuators are used to set up two-dimensional pneumatic arms, which are used mainly to simulate the excavator's motion. Fuzzy control algorithms are typically applied in pneumatic control systems owing to their non-linearities and ill-defined mathematical model. The self-organizing fuzzy controller, which includes a self-learning mechanism to modify fuzzy rules, is applied in these two-dimensional pneumatic arm control systems. Via a variety of trajectory tracking experiments, the present paper provides comparisons of system characteristics and control performances.

scholarly journals Pinhole-type two-dimensional ultra-small-angle X-ray scattering on the micrometer scale

2013 ◽  
Vol 21 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Hiroyuki Kishimoto ◽  
Yuya Shinohara ◽  
Yoshio Suzuki ◽  
Akihisa Takeuchi ◽  
Naoto Yagi ◽  
...  
Keyword(s):  
Small Angle ◽  
Two Dimensional ◽  
X Ray ◽  
X Ray Scattering ◽  
Detector Distance ◽  
Medium Length ◽  
Set Up ◽  
Micrometer Scale ◽  
Ray Scattering

A pinhole-type two-dimensional ultra-small-angle X-ray scattering set-up at a so-called medium-length beamline at SPring-8 is reported. A long sample-to-detector distance, 160.5 m, can be used at this beamline and a small-angle resolution of 0.25 µm−1was thereby achieved at an X-ray energy of 8 keV.

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