scholarly journals Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 53 ◽  
Author(s):  
Astrid Eichhorn ◽  
Tim Koslowski ◽  
Antonio Pereira
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Discrete Models ◽  
Practical Implementation ◽  
Tensor Model ◽  
Independent Form ◽  
Tensor Models

A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual ideas underlying the use of the number of degrees of freedom as a scale for a Renormalization Group flow. We focus on tensor models, for which we explain how the tensor size serves as the scale for a background-independent coarse-graining flow. This flow provides a new probe of a universal continuum limit in tensor models. We review the development and setup of this tool and summarize results in the two- and three-dimensional case. Moreover, we provide a step-by-step guide to the practical implementation of these ideas and tools by deriving the flow of couplings in a rank-4-tensor model. We discuss the phenomenon of dimensional reduction in these models and find tentative first hints for an interacting fixed point with potential relevance for the continuum limit in four-dimensional quantum gravity.

TENSOR MODEL FOR GRAVITY AND ORIENTABILITY OF MANIFOLD

1991 ◽  
Vol 06 (28) ◽  
pp. 2613-2623 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Quantum Gravity ◽  
Hermitian Matrix ◽  
Three Dimensional ◽  
Tensor Model ◽  
Two Dimensional ◽  
Tensor Models ◽  
Arbitrary Dimensions ◽  
Dynamical Triangulation ◽  
Hermitian Matrix Model ◽  
Special Case

We investigate the relation between rank-three tensor models and the dynamical triangulation model of three-dimensional quantum gravity, and discuss the orientability of the manifold and the corresponding tensor models. We generalize the orientable tensor models to arbitrary dimensions, which include the two-dimensional Hermitian matrix model as a special case.

scholarly journals Asymptotic Expansion of the Multi-Orientable Random Tensor Model

10.37236/4629 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Eric Fusy ◽  
Adrian Tanasa
Keyword(s):  
Asymptotic Expansion ◽  
Matrix Models ◽  
Three Dimensional ◽  
Natural Generalization ◽  
General Term ◽  
Tensor Model ◽  
Half Integer ◽  
Tensor Models ◽  
Random Tensor

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expanion in $N$, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.

ON THE PHASE DIAGRAM OF THREE-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (32) ◽  
pp. 3005-3014 ◽  
Author(s):  
D. V. BOULATOV ◽  
A. KRZYWICKI
Keyword(s):  
Phase Diagram ◽  
Quantum Gravity ◽  
Continuum Limit ◽  
Critical Line ◽  
Tricritical Point ◽  
Three Dimensional ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
The Right ◽  
Discrete Formulation

The phase diagram of three-dimensional (3d) simplicial quantum gravity is studied using the Monte–Carlo simulation method. It is found that the behavior of the entropy of manifolds, unambiguously defined in this discrete formulation, insures the existence of a vacuum, in spite of the Einstein action being bottomless. A critical line is found as well as some evidence for the existence of a tricritical point. Only to the right of this point, where the bare coupling of the Einstein term in the action is strong enough, a sensible continuum limit can possibly exist.

scholarly journals RADIATIVE CORRECTIONS IN VECTOR-TENSOR MODELS

2010 ◽  
Vol 25 (01) ◽  
pp. 163-169 ◽  
Author(s):  
A. BUCHEL ◽  
F. A. CHISHTIE ◽  
M. T. HANIF ◽  
S. HOMAYOUNI ◽  
JUNJI JIA ◽  
...  
Keyword(s):  
Tensor Field ◽  
Degrees Of Freedom ◽  
Mass Term ◽  
Tensor Model ◽  
Mass Generation ◽  
Tensor Models ◽  
Scalar Mass ◽  
Antisymmetric Tensor Field ◽  
Field Shift ◽  
Additional Coupling

We consider a two-form antisymmetric tensor field ϕ minimally coupled to a non-Abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term [Formula: see text] for the tensor field eliminates degrees of freedom associated with this field. Explicit one-loop calculations show that an additional coupling m Tr (ϕ ∧ F) (which can be eliminated classically by a tensor field shift) reintroduces tensor field degrees of freedom. We attribute this to the lack of the renormalizability in our vector-tensor model. We also explore a vector-tensor model with a tensor field scalar mass term [Formula: see text] and coupling m Tr (ϕ ∧ ⋆F). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

A method for autonomous collision-free navigation of a quadrotor UAV in unknown tunnel-like environments

Robotica ◽  
2021 ◽  
pp. 1-27
Author(s):  
Taha Elmokadem ◽  
Andrey V. Savkin
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Autonomous Underwater Vehicles ◽  
Three Dimensional ◽  
Underwater Vehicles ◽  
Practical Implementation ◽  
Challenging Problem ◽  
Quadrotor Uav ◽  
Navigation Algorithm ◽  
Aerial Vehicles ◽  
Quadrotor Uavs

Abstract Unmanned aerial vehicles (UAVs) have become essential tools for exploring, mapping and inspection of unknown three-dimensional (3D) tunnel-like environments which is a very challenging problem. A computationally light navigation algorithm is developed in this paper for quadrotor UAVs to autonomously guide the vehicle through such environments. It uses sensors observations to safely guide the UAV along the tunnel axis while avoiding collisions with its walls. The approach is evaluated using several computer simulations with realistic sensing models and practical implementation with a quadrotor UAV. The proposed method is also applicable to other UAV types and autonomous underwater vehicles.

An acoustic liner design methodology based on a statistical source model

2021 ◽  
pp. 1475472X2110238
Author(s):  
Douglas M Nark ◽  
Michael G Jones
Keyword(s):  
Design Methodology ◽  
Three Dimensional ◽  
Aircraft Engine ◽  
Flight Test ◽  
Source Model ◽  
Practical Implementation ◽  
Source Information ◽  
Fan Noise ◽  
Future Design ◽  
Acoustic Liner

The attenuation of fan tones remains an important aspect of fan noise reduction for high bypass ratio turbofan engines. However, as fan design considerations have evolved, the simultaneous reduction of broadband fan noise levels has gained interest. Advanced manufacturing techniques have also opened new possibilities for the practical implementation of broadband liner concepts. To effectively address these elements, practical acoustic liner design methodologies must provide the capability to efficiently predict the acoustic benefits of novel liner configurations. This paper describes such a methodology to design and evaluate multiple candidate liner configurations using realistic, three dimensional geometries for which minimal source information is available. The development of the design methodology has been guided by a series of studies culminating in the design and flight test of a low drag, broadband inlet liner. The excellent component and system noise benefits obtained in this test demonstrate the effectiveness of the broadband liner design process. They also illustrate the value of the approach in concurrently evaluating multiple liner designs and their application to various locations within the aircraft engine nacelle. Thus, the design methodology may be utilized with increased confidence to investigate novel liner configurations in future design studies.

scholarly journals MEASUREMENTS AND INFORMATION IN SPIN FOAM MODELS

2012 ◽  
Vol 27 (28) ◽  
pp. 1250164
Author(s):  
J. MANUEL GARCÍA-ISLAS
Keyword(s):  
Information Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Shannon Entropy ◽  
Three Dimensional ◽  
Spin Network ◽  
Spin Foam Models ◽  
Foam Model ◽  
Spin Foam Model ◽  
Spin Foam

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.

scholarly journals Asymmetry in Three-Dimensional Sprinting with and without Running-Specific Prostheses

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 580
Author(s):  
Anna Lena Emonds ◽  
Katja Mombaur
Keyword(s):  
Degrees Of Freedom ◽  
Body Position ◽  
Three Dimensional ◽  
Problem Formulation ◽  
Contact Phase ◽  
Individual Level ◽  
Lower Trunk ◽  
Floating Base ◽  
The Asymmetry ◽  
Limb Asymmetry

As a whole, human sprinting seems to be a completely periodic and symmetrical motion. This view is changed when a person runs with a running-specific prosthesis after a unilateral amputation. The aim of our study is to investigate differences and similarities between unilateral below-knee amputee and non-amputee sprinters—especially with regard to whether asymmetry is a distracting factor for sprint performance. We established three-dimensional rigid multibody models of one unilateral transtibial amputee athlete and for reference purposes of three non-amputee athletes. They consist of 16 bodies (head, ipper, middle and lower trunk, upper and lower arms, hands, thighs, shanks and feet/running specific prosthesis) with 30 or 31 degrees of freedom (DOFs) for the amputee and the non-amputee athletes, respectively. Six DOFs are associated with the floating base, the remaining ones are rotational DOFs. The internal joints are equipped with torque actuators except for the prosthetic ankle joint. To model the spring-like properties of the prosthesis, the actuator is replaced by a linear spring-damper system. We consider a pair of steps which is modeled as a multiphase problem with each step consisting of a flight, touchdown and single-leg contact phase. Each phase is described by its own set of differential equations. By combining motion capture recordings with a least squares optimal control problem formulation including constraints, we reconstructed the dynamics of one sprinting trial for each athlete. The results show that even the non-amputee athletes showed less symmetrical sprinting than expected when examined on an individual level. Nevertheless, the asymmetry is much more pronounced in the amputee athlete. The amputee athlete applies larger torques in the arm and trunk joints to compensate the asymmetry and experiences a destabilizing influence of the trunk movement. Hence, the inter-limb asymmetry of the amputee has a significant effect on the control of the sprint movement and the maintenance of an upright body position.

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