scholarly journals Superstring Backgrounds in String Geometry

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Masaki Honda ◽  
Matsuo Sato ◽  
Taiki Tohshima
Keyword(s):  
String Theory ◽  
Equations Of Motion ◽  
Type I ◽  
Classical Dynamics ◽  
Geometry Model ◽  
Single String ◽  
String Background

String geometry theory is a candidate of the nonperturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how superstring backgrounds are described in string geometry theory. In this paper, we show that all the type IIA, IIB, SO(32) type I, and SO(32) and E 8 × E 8 heterotic superstring backgrounds are embedded in configurations of the fields of a single string geometry model. In particular, we show that the configurations satisfy the equations of motion of the string geometry model in α ′ ⟶ 0 if and only if the embedded string backgrounds satisfy the equations of motion of the supergravities, respectively. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.

scholarly journals String backgrounds in string geometry

2020 ◽  
Vol 35 (27) ◽  
pp. 2050176
Author(s):  
Masaki Honda ◽  
Matsuo Sato
Keyword(s):  
String Theory ◽  
Equations Of Motion ◽  
Classical Dynamics ◽  
Geometry Model ◽  
String Background

String geometry theory is a candidate of the nonperturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how string backgrounds are described in string geometry theory. In this paper, we show that the string backgrounds are embedded in configurations of the fields of a string geometry model. Especially, we show that the configurations satisfy the equations of motion of the string geometry model if and only if the embedded string backgrounds satisfy their equations of motion. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.

scholarly journals The Fayet-Iliopoulos term in Type-I string theory and M-theory

1998 ◽  
Vol 437 (3-4) ◽  
pp. 318-324 ◽  
Author(s):  
John March-Russell
Keyword(s):  
String Theory ◽  
Type I ◽  
M Theory

scholarly journals Probing type I′i string theory using D0 and D4-branes

1997 ◽  
Vol 415 (2) ◽  
pp. 135-143 ◽  
Author(s):  
Justin R. David ◽  
Avinash Dhar ◽  
Gautam Mandal
Keyword(s):  
String Theory ◽  
Type I

scholarly journals D-Branes in Type I String Theory

2001 ◽  
Vol 49 (4-6) ◽  
pp. 503-510
Author(s):  
M. Frau ◽  
L. Gallot ◽  
A. Lerda ◽  
P. Strigazzi
Keyword(s):  
String Theory ◽  
Type I

Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers

2020 ◽  
pp. 2150016
Author(s):  
Mohsen Rahmani ◽  
Sajjad Dehghanpour
Keyword(s):  
Thermal Stresses ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Type I ◽  
Sandwich Beams ◽  
Temperature Dependent ◽  
The Core ◽  
Graded Layers ◽  
Lagrange Strain

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

Singularity robust balancing of parallel manipulators following inconsistent trajectories

Robotica ◽  
2014 ◽  
Vol 34 (9) ◽  
pp. 2027-2038 ◽  
Author(s):  
Mustafa Özdemir
Keyword(s):  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Type I ◽  
Type Ii ◽  
Inverse Dynamic ◽  
Serial Manipulators ◽  
Dynamic Solution ◽  
Singular Configuration ◽  
Kinematic Singularities

SUMMARYWhen compared to serial manipulators, parallel manipulators have small workspaces mainly due to their closed-loop structure. As opposed to type I singularities (or inverse kinematic singularities) that are generally encountered at the workspace boundaries, type II singularities characteristically arise within the workspace, and around them, the inverse dynamic solution becomes unbounded. Hence, a desired trajectory passing through a type II singular position cannot be achieved by the manipulator, and its useful workspace becomes further and substantially reduced. It has been previously shown in the literature that if the trajectory is replanned in such a way that the dynamic equations of motion of the manipulator are consistent at a type II singularity, i.e. if the trajectory is consistent, then the manipulator passes through this singular configuration in a controllable manner, while the inverse dynamic solution remains finite. An inconsistent trajectory, on the other hand, is stated in the literature to be unrealizable. However, although seems a promising technique, trajectory replanning itself is also a deviation from the originally desired trajectory, and there might be cases in applications where, due to some task-specific reasons, the desired trajectory, although inconsistent, is not allowed to be replanned to satisfy the consistency conditions. In this paper, a method of singularity robust balancing is proposed for parallel manipulators passing through type II singular configurations while following inconsistent trajectories. By this means, an originally unrealizable inconsistent trajectory passing through a type II singularity can be followed without any deviation, while the required actuator forces remain bounded after the manipulator is balanced according to the design methodology presented in this study. The effectiveness of the introduced method is shown through numerical simulations considering a planar 3-DOF 2-PRR parallel manipulator under different balancing scenarios.

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