Minimal curvature-constrained networks

The purpose of this paper is to discuss the perfect fluid gravitational collapse in modified f(R) metric gravity theories with non-minimal curvature coupled to matter. For this inference, we investigate the effects on self-gravitating implosion with spherically symmetric non-static geometry in the presence of extra force [Formula: see text], that express the cosmic expansion with dark source constraints. Matching conditions are given in which we have taken the insertion of non-static interior and static exterior regions along with cosmological constant. We have investigated the apparent horizons with effective results and along with their physical interpretation. It is analyzed that the extra component of dark source material reduces the gravitating implosion, hence slowing the rate of collapse. This study also reflects the contribution towards the perfect fluid for the generalization in f(R) gravity with zero coupling constant [Formula: see text].

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Blending Surfaces with Minimal Curvature

Graphics and Robotics ◽

10.1007/978-3-642-79210-6_10 ◽

1995 ◽

pp. 163-174 ◽

Cited By ~ 2

Author(s):

Günther Greiner

Keyword(s):

Minimal Curvature

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Neuron Net for Forming Optimal Smooth Trajectories Based on Bezier Splines

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.865.442 ◽

2017 ◽

Vol 865 ◽

pp. 442-449

Author(s):

Dmitry Yukhimets

Keyword(s):

Computational Complexity ◽

Real Time ◽

Optimal Selection ◽

Third Order ◽

The Third ◽

Maximal Speed ◽

Minimal Curvature ◽

Selection Of

In this paper, the problem of planning smooth trajectories of mechatronic objects on the basis of Bezier splines of the third order with a minimal curvature is solved. Using such trajectories provides the maximal speed of movement for mechatronic objects. The neuron net, which approximates the function of the optimal selection of spline parameters is proposed to solve this problem. The advantage of the proposed approach is its lack of computational complexity, which allows its use in most on-board computers in real time.

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Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics

Journal of Computational Physics ◽

10.1016/j.jcp.2010.05.008 ◽

2010 ◽

Vol 229 (18) ◽

pp. 6512-6533 ◽

Cited By ~ 15

Author(s):

Dirk Lebiedz ◽

Volkmar Reinhardt ◽

Jochen Siehr

Keyword(s):

Chemical Kinetics ◽

Riemannian Geometry ◽

Slow Manifold ◽

Minimal Curvature

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The Curvature of Lattice Knots

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216599000328 ◽

1999 ◽

Vol 08 (04) ◽

pp. 463-490 ◽

Cited By ~ 15

Author(s):

E. J. Janse van Rensburg ◽

S. D. Promislow

Keyword(s):

Total Curvature ◽

Cubic Lattice ◽

Minimal Curvature

A result of Milnor [1] states that the infimum of the total curvature of a tame knot K is given by 2πμ(K), where μ(K) is the crookedness of the knot K. It is also known that μ(K)=b(K), where b(K) is the bridge index of K [2]. The situation appears to be quite different for knots realised as polygons in the cubic lattice. We study the total curvature of lattice knots by developing algebraic techniques to estimate minimal curvature in the cubic lattice. We perform simulations to estimte the minimal curvature of lattice knots, and conclude that the situation is very different than for tame knots in ℛ3.

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THE MINIMAL CURVATURE OF THE UNIVERSE IN MODIFIED GRAVITY AND CONFORMAL ANOMALY RESOLUTION OF THE INSTABILITIES

Modern Physics Letters A ◽

10.1142/s0217732304013295 ◽

2004 ◽

Vol 19 (08) ◽

pp. 627-638 ◽

Cited By ~ 91

Author(s):

SHIN'ICHI NOJIRI ◽

SERGEI D. ODINTSOV

Keyword(s):

Dark Energy ◽

Modified Gravity ◽

Cosmic Acceleration ◽

Conformal Anomaly ◽

Frw Universe ◽

Conformal Fields ◽

Acceleration Of The Universe ◽

Minimal Curvature ◽

The Universe ◽

Universe Evolution

We discuss the modified gravity which may produce the current cosmic acceleration of the universe and eliminate the need for dark energy. It is shown that such models where the action quickly grows with the decrease of the curvature define the FRW universe with the minimal curvature. Infinite time is required to reach the minimal curvature during the universe evolution. It is demonstrated that quantum effects of conformal fields may strongly suppress the instabilities discovered in modified gravity. We also briefly speculate on the modification of gravity combined with the presence of the cosmological constant dark energy.

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PALATINI FORMULATION OF MODIFIED GRAVITY WITH A NON-MINIMAL CURVATURE-MATTER COUPLING

Modern Physics Letters A ◽

10.1142/s0217732311035869 ◽

2011 ◽

Vol 26 (20) ◽

pp. 1467-1480 ◽

Cited By ~ 53

Author(s):

TIBERIU HARKO ◽

TOMI S. KOIVISTO ◽

FRANCISCO S. N. LOBO

Keyword(s):

Energy Momentum Tensor ◽

Equations Of Motion ◽

Scalar Fields ◽

Momentum Tensor ◽

Nonlinear Dependence ◽

Modified Theories Of Gravity ◽

Field Equations ◽

Test Particles ◽

Theories Of Gravity ◽

Minimal Curvature

We derive the field equations and the equations of motion for scalar fields and massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi–Cività connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the nonconservation of the energy–momentum tensor. We derive 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 is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity. It is pointed out here that the force is of a different nature than in the metric formalism. We also consider the implications of a nonlinear dependence of the action upon the matter Lagrangian.

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