scholarly journals The emergence of expanding space–time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Kohta Hatakeyama ◽  
Akira Matsumoto ◽  
Jun Nishimura ◽  
Asato Tsuchiya ◽  
Atis Yosprakob
Keyword(s):  
Matrix Model ◽  
Classical Equation ◽  
Space Time ◽  
Descent Method ◽  
Classical Solutions ◽  
Gradient Descent Method ◽  
Infinite Matrix ◽  
Superstring Theory ◽  
Matrix Size ◽  
Monte Carlo Studies

Abstract The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. As such, it is expected to explain the origin of space–time and matter at the same time. This has been partially demonstrated by the previous Monte Carlo studies on the Lorentzian version of the model, which suggested the emergence of (3+1)-dimensional expanding space–time. Here we investigate the same model by solving numerically the classical equation of motion, which is expected to be valid at late times since the action becomes large due to the expansion of space. Many solutions are obtained by the gradient descent method starting from random matrix configurations, assuming a quasi-direct-product structure for the (3+1)-dimensions and the extra 6 dimensions. We find that these solutions generally admit the emergence of expanding space–time and a block-diagonal structure in the extra dimensions, the latter being important for the emergence of intersecting D-branes. For solutions corresponding to D-branes with appropriate dimensionality, the Dirac operator is shown to acquire a zero mode in the limit of infinite matrix size.

scholarly journals On the structure of the emergent 3D expanding space in the Lorentzian type IIB matrix model

2019 ◽  
Vol 2019 (9) ◽  
Author(s):  
Toshihiro Aoki ◽  
Mitsuaki Hirasawa ◽  
Yuta Ito ◽  
Jun Nishimura ◽  
Asato Tsuchiya
Keyword(s):  
Matrix Model ◽  
Space Time ◽  
Original Model ◽  
Regular Space ◽  
Superstring Theory ◽  
Pauli Matrices ◽  
Sign Problem ◽  
Monte Carlo Studies ◽  
Space Time Structure ◽  
Bosonic Part

Abstract The emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon that has been observed in Monte Carlo studies of this model. In particular, this may be taken as support for the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplified versions, and find that the expanding part of the space is described essentially by the Pauli matrices. We argue that this is due to an approximation used in the simulation to avoid the sign problem, which actually amounts to replacing ${e}^{iS_{\rm b}}$ by ${e}^{\beta S_{\rm b}}$ ($\beta>0$) in the partition function, where $S_{\rm b}$ is the bosonic part of the action. We also discuss the possibility of obtaining a regular space-time with the (3+1)D expanding behavior in the original model with the correct ${e}^{iS_{\rm b}}$ factor.

scholarly journals CLASSICAL SOLUTIONS IN THE LORENTZIAN MATRIX MODEL FOR SUPERSTRING THEORY

2013 ◽  
Vol 21 ◽  
pp. 197-199
Author(s):  
SANG-WOO KIM ◽  
JUN NISHIMURA ◽  
ASATO TSUCHIYA
Keyword(s):  
Monte Carlo ◽  
Matrix Model ◽  
Rotational Symmetry ◽  
Monte Carlo Study ◽  
Spontaneous Breaking ◽  
Classical Solutions ◽  
Superstring Theory ◽  
Numerical Result ◽  
Complementary Approach

Recent Monte Carlo study on the Lorentzian matrix model for superstring theory revealed that an expanding (3 + 1)d universe appears dynamically from (9 + 1)d. The mechanism for the spontaneous breaking of rotational symmetry relies crucially on the noncommutative nature of the three expanding spaces. As a complementary approach to possible future beyond the numerical result, we discuss classical solutions for the Lorentzian matrix model and their properties.

scholarly journals Mesoscale Modelling of Concretes Subjected to Triaxial Loadings: Mechanical Properties and Fracture Behaviour

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1099
Author(s):  
Qingqing Chen ◽  
Yuhang Zhang ◽  
Tingting Zhao ◽  
Zhiyong Wang ◽  
Zhihua Wang
Keyword(s):  
Mechanical Properties ◽  
Tensile Stress ◽  
Failure Criterion ◽  
Mesoscale Model ◽  
Fracture Behaviour ◽  
Descent Method ◽  
Triaxial Stress ◽  
Gradient Descent Method ◽  
Stress States ◽  
Shear Failures

The mechanical properties and fracture behaviour of concretes under different triaxial stress states were investigated based on a 3D mesoscale model. The quasistatic triaxial loadings, namely, compression–compression–compression (C–C–C), compression–tension–tension (C–T–T) and compression–compression–tension (C–C–T), were simulated using an implicit solver. The mesoscopic modelling with good robustness gave reliable and detailed damage evolution processes under different triaxial stress states. The lateral tensile stress significantly influenced the multiaxial mechanical behaviour of the concretes, accelerating the concrete failure. With low lateral pressures or tensile stress, axial cleavage was the main failure mode of the specimens. Furthermore, the concretes presented shear failures under medium lateral pressures. The concretes experienced a transition from brittle fracture to plastic failure under high lateral pressures. The Ottosen parameters were modified by the gradient descent method and then the failure criterion of the concretes in the principal stress space was given. The failure criterion could describe the strength characteristics of concrete materials well by being fitted with experimental data under different triaxial stress states.

scholarly journals Fuzzy Formation Control and Collision Avoidance for Multiagent Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Yeong-Hwa Chang ◽  
Chun-Lin Chen ◽  
Wei-Shou Chan ◽  
Hung-Wei Lin ◽  
Chia-Wen Chang
Keyword(s):  
Collision Avoidance ◽  
Multiagent Systems ◽  
Formation Control ◽  
Descent Method ◽  
Minimum Problem ◽  
Gradient Descent Method ◽  
Consensus Formation ◽  
Distributed Information ◽  
Graph Theoretic ◽  
Learning Rules

This paper aims to investigate the formation control of leader-follower multiagent systems, where the problem of collision avoidance is considered. Based on the graph-theoretic concepts and locally distributed information, a neural fuzzy formation controller is designed with the capability of online learning. The learning rules of controller parameters can be derived from the gradient descent method. To avoid collisions between neighboring agents, a fuzzy separation controller is proposed such that the local minimum problem can be solved. In order to highlight the advantages of this fuzzy logic based collision-free formation control, both of the static and dynamic leaders are discussed for performance comparisons. Simulation results indicate that the proposed fuzzy formation and separation control can provide better formation responses compared to conventional consensus formation and potential-based collision-avoidance algorithms.

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