scholarly journals Cosmic voids and filaments from quantum gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
J. Ambjørn ◽  
Z. Drogosz ◽  
J. Gizbert-Studnicki ◽  
A. Görlich ◽  
J. Jurkiewicz ◽  
...  
Keyword(s):  
Quantum Gravity ◽  
Boundary Conditions ◽  
Computer Simulations ◽  
Laplace Equation ◽  
Scalar Fields ◽  
Coordinate Condition ◽  
Quantum Universe ◽  
D 43 ◽  
Close Analogue ◽  
Harmonic Coordinate

AbstractUsing computer simulations, we study the geometry of a typical quantum universe, i.e., the geometry one might expect before a possible period of inflation. We display it using coordinates defined by means of four classical scalar fields satisfying the Laplace equation with nontrivial boundary conditions. They are a close analogue of the harmonic coordinate condition used in the context of GR (Kuchar and Torre in Phys Rev D 43:419–441, 1991). It is highly nontrivial that these ideas can be applied to understand the structures which appear in very irregular and fluctuating geometries. The field configurations reveal cosmic web structures surprisingly similar to the ones observed in the present-day universe.

scholarly journals Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 45
Author(s):  
Christof Wetterich
Keyword(s):  
Quantum Gravity ◽  
Top Quark ◽  
Particle Physics ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Standard Model ◽  
Scaling Potential ◽  
Realistic Description ◽  
The Masses ◽  
Dynamical Dark Energy

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.

Hydrodynamic Coupling of Viscous and Non-Viscous Numerical Wave Solutions Within the Open-Source Hydrodynamics Framework REEF3D

2021 ◽  
Author(s):  
Weizhi Wang ◽  
Csaba Pákozdi ◽  
Arun Kamath ◽  
Tobias Martin ◽  
Hans Bihs
Keyword(s):  
High Resolution ◽  
Boundary Conditions ◽  
Open Source ◽  
Laplace Equation ◽  
Scale Model ◽  
Surface Boundary ◽  
Cfd Model ◽  
Hydrodynamic Coupling ◽  
Coupling Strategy ◽  
Numerical Wave

Abstract A comprehensive understanding of the marine environment in the offshore area requires phase-resolved wave information. For the far-field wave propagation, computational efficiency is crucial, as large spatial and temporal scales are involved. For the near-field extreme wave events and wave impacts, high resolution is required to resolve the flow details and turbulence. The combined use of a computationally efficient large-scale model and a high-resolution local-scale solver provides a solution the combines accuracy and efficiency. This article introduces a coupling strategy between the efficient fully nonlinear potential flow (FNPF) solver REEF3D::FNPF and the high-fidelity computational fluid dynamics (CFD) model REEF3D::CFD within in the open-source hydrodynamics framework REEF3D. REEF3D::FNPF solves the Laplace equation together with the boundary conditions on a sigma-coordinate. The free surface boundary conditions are discretised using high-order finite difference methods. The Laplace equation for the velocity potential is solved with a conjugated gradient solver preconditioned with geometric multi-grid provided by the open-source library hypre. The model is fully parallelised following the domain decomposition strategy and the MPI protocol. The waves calculated with the FNPF solver are used as wave generation boundary condition for the CFD based numerical wave tank REEF3D::CFD. The CFD model employs an interface capturing two-phase flow approach that can resolve complex wave structure interaction, including breaking wave kinematics and turbulent effects. The presented hydrodynamic coupling strategy is tested for various wave conditions and the accuracy is fully assessed.

scholarly journals Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

2005 ◽  
Vol 22 (6) ◽  
pp. 957-974 ◽  
Author(s):  
Giampiero Esposito ◽  
Guglielmo Fucci ◽  
Alexander Yu Kamenshchik ◽  
Klaus Kirsten
Keyword(s):  
Quantum Gravity ◽  
Boundary Conditions ◽  
Spectral Asymptotics

scholarly journals Stability and boundedness in AdS/CFT with double trace deformations

2019 ◽  
Vol 34 (18) ◽  
pp. 1950138 ◽  
Author(s):  
Steven Casper ◽  
William Cottrell ◽  
Akikazu Hashimoto ◽  
Andrew Loveridge ◽  
Duncan Pettengill
Keyword(s):  
Renormalization Group ◽  
Boundary Conditions ◽  
Vector Fields ◽  
Scalar Fields ◽  
Legendre Transform ◽  
Renormalization Group Flow ◽  
Physical Content ◽  
Effective Masses ◽  
Group Flow

Scalar fields on the bulk side of AdS/CFT correspondence can be assigned unconventional boundary conditions related to the conventional one by Legendre transform. One can further perform double trace deformations which relate the two boundary conditions via renormalization group flow. Thinking of these operators as S and T transformations, respectively, we explore the SL(2, R) family of models which naively emerges from repeatedly applying these operations. Depending on the parameters, the effective masses vary and can render the theory unstable. However, unlike in the SL(2, Z) structure previously seen in the context of vector fields in AdS4, some of the features arising from this exercise, such as the vacuum susceptibility, turns out to be scheme dependent. We explain how scheme independent physical content can be extracted in spite of some degree of scheme dependence in certain quantities.

scholarly journals A computing method for bending problem of thin plate on Pasternak foundation

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093933
Author(s):  
Jiarong Gan ◽  
Hong Yuan ◽  
Shanqing Li ◽  
Qifeng Peng ◽  
Huanliang Zhang
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Integral Equations ◽  
Thin Plate ◽  
Laplace Equation ◽  
Two Dimensional ◽  
Pasternak Foundation ◽  
Helmholtz Operator ◽  
Numerical Computing ◽  
Matlab Programming

The governing equation of the bending problem of simply supported thin plate on Pasternak foundation is degraded into two coupled lower order differential equations using the intermediate variable, which are a Helmholtz equation and a Laplace equation. A new solution of two-dimensional Helmholtz operator is proposed as shown in Appendix 1. The R-function and basic solutions of two-dimensional Helmholtz operator and Laplace operator are used to construct the corresponding quasi-Green function. The quasi-Green’s functions satisfy the homogeneous boundary conditions of the problem. The Helmholtz equation and Laplace equation are transformed into integral equations applying corresponding Green’s formula, the fundamental solution of the operator, and the boundary condition. A new boundary normalization equation is constructed to ensure the continuity of the integral kernels. The integral equations are discretized into the nonhomogeneous linear algebraic equations to proceed with numerical computing. Some numerical examples are given to verify the validity of the proposed method in calculating the problem with simple boundary conditions and polygonal boundary conditions. The required results are obtained through MATLAB programming. The convergence of the method is discussed. The comparison with the analytic solution shows a good agreement, and it demonstrates the feasibility and efficiency of the method in this article.

On the vacuum stress induced by uniform acceleration or supporting the ether

1977 ◽  
Vol 354 (1676) ◽  
pp. 79-99 ◽  
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Scalar Fields ◽  
Black Body ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Perfect Conductor ◽  
Infinite Plane ◽  
Uniform Acceleration

The stresses induced in the vacuum by the uniform acceleration of an infinite plane conductor are computed for the massless scalar and electromagnetic fields. Both Dirichlet and Neumann boundary conditions are considered for the scalar field; far from the conductor it is found, independently of the boundary condition, that the vacuum stress is ‘local’ and corresponds to the absence from the vacuum of black body radiation. Approaching the conductor, the energy density in the Dirichlet case is slightly lower than the ‘local’ term, and in the Neumann case slightly higher. At very small distances it again has the same asymptotic form for both scalar fields. For the electromagnetic field the results are similar to those for the scalar field with Dirichlet boundary conditions. Far from the conductor the spectrum is again black-body, though not Planckian. In all cases the acausal nature of ‘ perfect conductor ’ boundary conditions prevents the stress tensor from being finite on the conductor.

scholarly journals CLASSICALLY INTEGRABLE FIELD THEORIES WITH DEFECTS

2004 ◽  
Vol 19 (supp02) ◽  
pp. 82-91 ◽  
Author(s):  
P. BOWCOCK ◽  
E. CORRIGAN ◽  
C. ZAMBON
Keyword(s):  
Integrable Field Theories ◽  
Boundary Conditions ◽  
Scalar Fields ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Internal Boundary ◽  
Liouville Type ◽  
Real Scalar ◽  
Integrable Field

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.

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