scholarly journals Leaps and bounds towards scale separation

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
G. Bruno De Luca ◽  
Alessandro Tomasiello
Keyword(s):  
Ricci Tensor ◽  
Broad Class ◽  
Equations Of Motion ◽  
Internal Diameter ◽  
Warping Function ◽  
Local Behavior ◽  
Scale Separation ◽  
Planck Mass ◽  
Curvature Bound ◽  
Gravity Theories

Abstract In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry-Émery geometry, we put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter. We reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. We find that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.

CLASSICAL SOLUTIONS OF THE p-BRANES

1989 ◽  
Vol 04 (13) ◽  
pp. 1287-1295 ◽  
Author(s):  
D.T. STOYANOV
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
General Class ◽  
Broad Class ◽  
Equations Of Motion ◽  
Classical Solutions ◽  
Subsidiary Condition ◽  
Nonlinear Equations Of Motion

An appropriate subsidiary condition is introduced in the classical actions of the p-branes (p arbitrary). A general class of exact solutions of the resulting nonlinear equations of motion are obtained which yield a broad class of characteristics for the original covariant equations of the p-branes.

Dispersion of Torsional Waves in Uniform Elastic Rods

1974 ◽  
Vol 41 (4) ◽  
pp. 1041-1046 ◽  
Author(s):  
O. L. Engstro¨m
Keyword(s):  
Finite Element Method ◽  
Cross Sections ◽  
Equations Of Motion ◽  
Order Theory ◽  
Warping Function ◽  
Elastic Rods ◽  
The Finite Element Method ◽  
Torsional Waves ◽  
Approximate Equations ◽  
Low Order

Approximate equations of motion are derived by use of Hamilton’s variational principle. The warping function, which is part of the solution, depends on wavelength. Numerical results on dispersion for rectangular cross sections have been obtained by the finite-element method. A comparison with the experimentally verified Barr theory is given. The paper is a contribution to the low-order approximate theories of torsional waves. It shows how good the Saint Venant warping function assumption in the low-order theory is at long relative wavelengths and it provides a modification of the theory for use at shorter wavelengths.

scholarly journals New de Sitter solutions in ten dimensions and orientifold singularities

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Clay Córdova ◽  
G. Bruno De Luca ◽  
Alessandro Tomasiello
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Local Behavior ◽  
De Sitter

Abstract In previous work, we found ten-dimensional solutions to the supergravity equations of motion with a dS4 factor and O8-planes. We generalize this analysis and obtain other solutions in the same spirit, with an O8+ and an O6−. We examine our original solutions in more detail, focusing in particular on the O8− singularities and on the issues created by their boundary conditions. We also point out some previously known super- symmetric AdS solutions with the same local behavior at their O8− singularity.

scholarly journals Thermodynamic properties of modified gravity theories

2016 ◽  
Vol 13 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Kazuharu Bamba
Keyword(s):  
Thermodynamic Properties ◽  
Modified Gravity ◽  
Equations Of Motion ◽  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Modified Gravity Theories ◽  
Gravity Theories ◽  
Clausius Relation ◽  
The Universe

We review thermodynamic properties of modified gravity theories, such as [Formula: see text] gravity and [Formula: see text] gravity, where [Formula: see text] is the scalar curvature and [Formula: see text] is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in [Formula: see text] gravity. We show both equilibrium and nonequilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met, when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.

scholarly journals TWO-SCALE MICROSTRUCTURE DYNAMICS

2011 ◽  
Vol 03 (03) ◽  
pp. 177-188
Author(s):  
ARKADI BEREZOVSKI ◽  
MIHHAIL BEREZOVSKI ◽  
JÜRI ENGELBRECHT
Keyword(s):  
Wave Propagation ◽  
Equations Of Motion ◽  
Dispersion Curves ◽  
Linear Momentum ◽  
Internal Variables ◽  
Type Model ◽  
Length Scale ◽  
Scale Separation ◽  
Dual Internal Variables

Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlin-type model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out.

scholarly journals Convective Self-Aggregation and Tropical Cyclogenesis under the Hypohydrostatic Rescaling

2016 ◽  
Vol 73 (2) ◽  
pp. 525-544 ◽  
Author(s):  
William R. Boos ◽  
Alexey Fedorov ◽  
Les Muir
Keyword(s):  
Tropical Cyclones ◽  
Gravity Waves ◽  
Equations Of Motion ◽  
Horizontal Resolution ◽  
Explicit Representation ◽  
Tropical Cyclogenesis ◽  
Single Model ◽  
Scale Separation ◽  
Self Aggregation ◽  
Dry Bias

Abstract The behavior of rotating and nonrotating aggregated convection is examined at various horizontal resolutions using the hypohydrostatic, or reduced acceleration in the vertical (RAVE), rescaling. This modification of the equations of motion reduces the scale separation between convective- and larger-scale motions, enabling the simultaneous and explicit representation of both types of flow in a single model without convective parameterization. Without the RAVE rescaling, a dry bias develops when simulations of nonrotating radiative–convective equilibrium are integrated at coarse resolution in domains large enough to permit convective self-aggregation. The rescaling reduces this dry bias, and here it is suggested that the rescaling moistens the troposphere by weakening the amplitude and slowing the group velocity of gravity waves, thus reducing the subsidence drying around aggregated convection. Separate simulations of rotating radiative–convective equilibrium exhibit tropical cyclogenesis; as horizontal resolution is coarsened without the rescaling, the resulting storms intensify more slowly and achieve lower peak intensities. At a given horizontal resolution, using RAVE increases peak storm intensity and reduces the time needed for tropical cyclogenesis—effects here suggested to be caused at least in part by the environmental moistening produced by RAVE. Consequently, the RAVE rescaling has the potential to improve simulations of tropical cyclones and other aggregated convection in models with horizontal resolutions of order 10–100 km.

A Newtonian mechanics formulation for the vibration of translating and rotating elastic continua

2019 ◽  
Vol 25 (10) ◽  
pp. 1639-1652 ◽  
Author(s):  
Robert L Lowe ◽  
Christopher G Cooley
Keyword(s):  
Control Volume ◽  
Broad Class ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Integral Form ◽  
Newtonian Mechanics ◽  
Elastic Continuum ◽  
Rotating Systems ◽  
Axially Moving ◽  
Kinematics And Kinetics

In this paper, we present a Newtonian mechanics formulation for modeling the vibration of a convecting elastic continuum, i.e., a system characterized by mean kinematic translation or rotation with small superposed vibrations. The proposed Newtonian approach complements customary energy-based techniques and serves as a convenient means to validate and physically interpret their results. We develop the equations of motion and matching conditions in a continuum mechanics setting with respect to a stationary inertial reference frame. Interaction of the convecting continuum with discrete space-fixed elements (e.g., springs and dampers) is enabled, without introducing time-dependent coefficients, through the use of Eulerian kinematics and kinetics. Kinematic discontinuities inherent in these interactions are accommodated by employing a global (or integral) form of balance of linear momentum applied to a space-fixed control volume. A generalized form of Navier's equation of elastic wave propagation is derived, with unsteady, Coriolis, centripetal, and convective contributions to the inertia. The resulting formulation is applied to a broad class of translating and rotating systems – including spinning rings, axially moving strings and beams, and general three-dimensional elastic structures – and shown to successfully reconcile with existing energy-based derivations in the literature.

scholarly journals Noether Currents and Maxwell-Type Equations of Motion in Higher Derivative Gravity Theories

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1408
Author(s):  
Taichiro Kugo
Keyword(s):  
Field Equation ◽  
Linear Combination ◽  
Source Term ◽  
Equations Of Motion ◽  
High Order Derivative ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Brs Symmetry ◽  
Noether Current ◽  
Global Translation

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s IOSp(8|8) choral symmetry containing the BRS symmetry as its member are constructed. We generally show that for each of these Noether currents, a suitable linear combination of equations of motion can be brought into the form of a Maxwell-type field equation possessing the Noether current as its source term.

Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems With Application to Direct Optimal Control

2018 ◽  
Vol 13 (10) ◽  
Author(s):  
Staffan Björkenstam ◽  
Sigrid Leyendecker ◽  
Joachim Linn ◽  
Johan S. Carlson ◽  
Bengt Lennartson
Keyword(s):  
Optimal Control ◽  
Multibody Systems ◽  
Inverse Dynamics ◽  
Broad Class ◽  
Equations Of Motion ◽  
Human Motion ◽  
Planning Problem ◽  
Unit Quaternions ◽  
Rigid Multibody Systems ◽  
Digital Human

In this paper, we present efficient algorithms for computation of the residual of the constrained discrete Euler–Lagrange (DEL) equations of motion for tree structured, rigid multibody systems. In particular, we present new recursive formulas for computing partial derivatives of the kinetic energy. This enables us to solve the inverse dynamics problem of the discrete system with linear computational complexity. The resulting algorithms are easy to implement and can naturally be applied to a very broad class of multibody systems by imposing constraints on the coordinates by means of Lagrange multipliers. A comparison is made with an existing software package, which shows a drastic improvement in computational efficiency. Our interest in inverse dynamics is primarily to apply direct transcription optimal control methods to multibody systems. As an example application, we present a digital human motion planning problem, which we solve using the proposed method. Furthermore, we present detailed descriptions of several common joints, in particular singularity-free models of the spherical joint and the rigid body joint, using the Lie groups of unit quaternions and unit dual quaternions, respectively.

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