Boundary Of Spacetime Research Articles

Fully discrete Schwarz waveform relaxation analysis for the heat equation on a finite spatial domain

Schwarz waveform relaxation methods provide space-time parallelism for the solution of time dependent partial differential equations. The algorithms are differentiated by the choice of the transmission conditions enforced at the introduced space-time boundaries. Early results considered the theoretical analysis of these algorithms in the continuous and semi-discrete (in space) settings for various families of linear partial differential equations. Later, fully discrete results were obtained under the simplifying assumption of an infinite spatial domain. In this paper, we provide a first analysis of a fully discrete classical Schwarz Waveform algorithm for the one-dimensional heat equation on an arbitrary but finite number of bounded subdomains. The θ-method is chosen as the time integrator. Convergence results are given in both the infinity norm and two norm, with an explicit contraction given in the case of a uniform partitioning. The results are compared to the numerics and to the earlier theoretical results.

Chiral Loop Quantum Supergravity and Black Hole Entropy

Recent work has shown that local supersymmetry on a spacetime boundary in N-extended AdS supergravity in chiral variables implies coupling to a boundary OSp(N|2)C super Chern–Simons theory. Consequently there has been a proposal to define and calculate the entropy S for the boundary, in the supersymmetric version of loop quantum gravity, for the minimal case N=1, via this super Chern–Simons theory. We give an overview of how supergravity can be treated in loop quantum gravity. We review the calculation of the dimensions of the quantum state spaces of UOSp(1|2) super Chern–Simons theory with punctures, and its analytical continuation, for the fixed quantum super area of the surface, to OSp(1|2)C. The result is S=aH/4 for large (super) areas. Lower order corrections can also be determined. We begin also a discussion of the statistical mechanics of the surface degrees of freedom by calculating the grand canonical partition function at zero chemical potential. This is a new result.

Acceleration of the space–time boundary element method using GPUs

Matrices arising from the space–time boundary element method for the heat equation are dense and are global in space and time. Thus, they require a large amount of memory which may pose a problem when accelerating the code using GPUs. In this paper, we present a method that overcomes this issue by assembling elements of system matrices only when needed during matrix–vector multiplication. Although this requires a significantly larger amount of floating-point operations when the matrix is repeatedly applied, due to the large processing power of modern GPUs, we are still able to achieve a significant speedup compared to the original CPU code.

The Analytic Wavefunction

The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an off-shell wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes.

Establishment of Creative Convergence Curriculum for Systematic Management of MZ Generation

A new generation of creativity (New-Collar) has arrived, not White-Collar or Blue-Collar. The main characteristics of the creative generation are the Fourth Industrial Revolution, the generation that makes good use of digital content and digital devices, expresses their tastes and colors well, and produces and consumes new things. Interest in Metaverse education that is scalable and realistic beyond space-time boundaries is growing, with the advent of the new normal era, in which non-face-to-face training has become every day’s work. With the technology development, the emergence of new educational services, and the changes in the environment at that time, the Metaverse education develops in various forms and is used in a variety of meanings. For this motivation, this study intends to examine earlier studies including curriculum procedures and present a model for creating a future creative convergence theme through a questionnaire. In addition, we intend to create a blueprint for convergence of university creativity and develop a plan to promote the design of creative convergence themes for the digital generation. This study is intended to help educational institutions think about designing curricula for the digital generation.

A novel meshfree method for investigating the impact of transverse joints quality on Xiaowan arch dam model

This paper presents a novel boundary collocation meshfree approach—space–time boundary moving least squares (BMLS) method to investigate the impact of transverse joints quality on the static and dynamic responses of a Xiaowan arch dam model. The proposed approach utilizes the space–time boundary moving least squares (BMLS) method based on one-dimensional moving least squares (MLS) technique to construct approximation formulas for solving three-dimensional elastic dynamic problems. Two models of Xiaowan arch dam, one with transverse joints and one without, were analyzed using the BMLS method to analyze the impact of transverse joint quality on the stability of the arch dam model. The numerical results suggest that the model with transverse joints already has good integrity when the ratio of the elastic modulus at the transverse joints to the elastic modulus of the dam material is 0.6. These findings demonstrate the promising development prospect of the BMLS method in practical engineering applications.

Airfoil trailing-edge noise prediction based on CFD/CAA coupled boundary method

Flow-induced noise hybrid prediction method based on sound wave boundary condition is an effective numerical method to deal with a flow-induced noise problems of complex configuration. This method can not only finely simulate the sound source, but also analyze the noise propagation characteristics. In this paper, numerical methods such as space-time discrete scheme and boundary conditions involved in discrete solution of acoustic perturbation equations(APE) are developed, and strategies such as adding buffer layer are proposed to improve divergence caused by numerical discontinuity at the junction of sound source region and propagation region, so as to establish a high-precision flow-induced noise hybrid method. In order to study the rationality of flow-induced noise hybrid method, the numerical simulation of acoustic radiation at the trailing edge of NACA0012 airfoil in BANC experiment was carried out. Compared with the results of sound field solved by large eddy simulation method, the analysis shows that the high-precision flow-induced noise hybrid method based on sound wave boundary conditions can predict the spatial sound field distribution with high precision and directly reflect the interaction between sound waves. Compared with the results of large eddy simulation, the error of sound pressure level is less than 2 dB, and the noise directional distribution trend is consistent.

A Phenomenological Study on the Experience of Learning Instrumental Music through Media in Youth

본 연구는 청소년이 경험한 미디어 기반 기악학습의 의미를 현상학적 질적 연구 방법을 사용하여 탐색하는 것에 그 목적을 둔다. 이를 위해 미디어를 통한 기악학습 경험이 있는 초등학생 2명, 고등학생 2명, 대학생 1명, 총 5명을 대상으로 리코더, 피아노, 기타, 플루트 관련 YouTube채널 활용에 대한 반구조화된 질문을 Zoom 화상 인터뷰로 진행하였고 수집된 자료를 현상학적 관점으로 분석하였다. 연구 결과 미디어를 통한 기악학습의 의미는 자신만의 목표에 따라 선정된 각기 다른 출발점, 시공간과 학습 수준의 경계를 넘나드는 접근의 편리함, 완성된 예제와의 즉각적인 비교를 통한 실력 향상, 미디어를 통한 기악학습 과정에서의 어려움과 문제해결을 위한 노력, 새로운 과제 도전에 대한 욕구로 나타났다. 이와 같은 연구 결과를 통해 미디어를 통한 기악학습에서는 전통적인 도제식 기악학습의 환경에서와는 차별화 되어 학습자 스스로 학습 목표를 설정하고 적절한 출발점을 직접 선택하며 본인이 처한 환경에 맞추어 능동적인 학습이 가능하며 이를 통한 성장의 가능성을 확인할 수 있었다.This study aims to explore the meaning of media-based instrumental learning experienced by youth using phenomenological qualitative research methods. To this end, a total of five elementary school students, two high school students, and one college student, who had experience in instrumental music learning through media, were asked semi-structured questions about the use of YouTube channels related to recorders, piano, guitar, and flute through Zoom video interviews, and the collected data were analyzed from a phenomenological perspective. As a result of the research, the instrumental music learning through media was shown as meaningful for various starting points specific to one's own goals, convenience of access regardless of space-time or learning level boundaries, improvement of skills through instant comparison with completed examples, efforts to solve difficulties and problems in the process of instrumental music learning through media, and desire to challenge new tasks. Through the results of such research, it was confirmed that instrumental music learning through media, which is different from the traditional apprenticeship instrumental learning environment, can enable learners to set their own learning goals, choose the appropriate starting point, and actively learn according to their environment, and grow through this.

Energy of the boundary of spacetime

Abstract We consider how the energy can be stored in the boundary of spacetime, in particular in a spherical bubble that can be made by a quantum gravitational process. Our calculation is performed within the framework of classical Einstein gravity by identifying the Gibbons–Hawking–York term as the membrane action. We show that the energy of the bubble can be given consistently with the Schwarzschild metric. The solution of the consistency condition suggests positive membrane tension, which explains why we do not observe such topological defects in ordinary experiences and also gives a mechanism for suppressing the spacetime with the boundary in a dynamical way.

Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions

We study a quantum scalar field, with general mass and coupling to the scalar curvature, propagating on three-dimensional global anti-de Sitter space-time. We determine the vacuum and thermal expectation values of the square of the field, also known as the vacuum polarisation (VP). We consider values of the scalar field mass and coupling for which there is a choice of boundary conditions giving well-posed classical dynamics. We apply Dirichlet, Neumann and Robin (mixed) boundary conditions to the field at the space-time boundary. We find finite values of the VP when the parameter governing the Robin boundary conditions is below a certain critical value. For all couplings, the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximal symmetry of the background space-time. However, this is not the case for Robin boundary conditions, when both the vacuum and thermal expectation values depend on the space-time location. At the space-time boundary, we find that both the vacuum and thermal expectation values of the VP with Robin boundary conditions converge to the result when Neumann boundary conditions are applied, except in the case of Dirichlet boundary conditions.

A Time-Adaptive Space-Time FMM for the Heat Equation

Abstract We present a new time-adaptive FMM for a space-time boundary element method for the heat equation. The method extends the existing parabolic FMM by adding new operations that allow for an efficient treatment of tensor product meshes which are adaptive in time. We analyze the efficiency of the new operations and the approximation quality of the related kernel expansions and present numerical experiments that reveal the benefits of the new method.

Fixing cosmological constant on the event horizon

Standard cosmological equations are written for the Hubble volume, while the real boundary of space-time is the event horizon. Within the unimodular and thermodynamic approaches to gravity, the dark energy term in cosmological equations appears as an integration constant, which we fix at the event horizon and obtain the observed value for the cosmological constant.

Upon the horizon’s verge: Thermal particle creation between and approaching horizons

Quantum particle creation from spacetime horizons, or accelerating boundaries in the dynamical Casimir effect, can have an equilibrium, or thermal, distribution. Using an accelerating boundary in flat spacetime (moving mirror), we investigate the production of thermal energy flux despite non-equilibrium accelerations, the evolution between equilibrium states, and the ‘interference’ between horizons. In particular, this allows us to give a complete solution to the particle spectrum of the accelerated boundary correspondence with Schwarzschild–de Sitter spacetime.

On a time-discrete convolution—space collocation BEM for the numerical solution of two-dimensional wave propagation problems in unbounded domains

Abstract For the numerical solution of a classical two-dimensional Dirichlet exterior problem for the wave equation in the time domain, we consider a space-time boundary integral equation approach, based on its discretization by means of the coupling of a time discrete convolution quadrature of order 2, with the classical continuous piecewise linear boundary element method. The latter is either the Galerkin method or the collocation one, this being computationally much cheaper. For the efficient evaluation of most of the integrals generated by these two boundary element methods, but also for the subsequent analysis, we first define a new Gaussian quadrature. After recalling that stability and convergence have been proved for the Galerkin method, while for the collocation one we only have numerical evidences of these properties, to (partially) fill this gap, we first note that collocation can be obtained directly from the Galerkin system, after discretizing its inner product integral by using the composite trapezoidal rule, which in this case turns out to be the Gaussian rule mentioned above with $1$ node. Then, we show that for all (positive) time step-sizes $\varDelta _t$, when we let $h\rightarrow 0$, independently from $\varDelta _t$, the matrix of the linear system produced by the collocation method, properly normalized, converges, in the $\infty $-norm, to the corresponding Galerkin matrix. The behavior of the associated absolute and relative errors in the $\infty $-norm, as $h\rightarrow 0$, are $O\big (h^{\frac {5}{3}}+\varDelta _t^{-(1+\varepsilon )}h^{\frac {5+\varepsilon }{2}}[|\!\ln \varDelta _t|+|\!\ln h|]\big )$ and $O\big (h^{\frac {2}{3}}/|\!\ln \varDelta _t|+\varDelta _t^{-(1+\varepsilon )}h^{\frac {3+\varepsilon }{2}}[1+|\!\ln h|/|\!\ln \varDelta _t|]\big )$, respectively, with $\varepsilon>0$ as close as one likes to $0$ and the $O(\cdot )$ constant independent from $\varDelta _t, h$. Some possible extensions of the investigation we carried out are also mentioned.

The holographic entropy cone from marginal independence

The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the holographic entropy cone, for an arbitrary number of parties, can be reconstructed from more fundamental data determined solely by subadditivity of quantum entropy. We formulate certain conjectures about graph models of holographic entanglement, for which we provide strong evidence, and rigorously prove that they all imply that such a reconstruction is possible. Our conjectures (except only for the weakest) further imply that the necessary data is remarkably simple. In essence, all one needs to know to reconstruct the holographic entropy cone, is a certain subset of the extreme rays of this simpler “subadditivity cone”, namely those which can be realized in holography. This recasting of the bewildering entanglement structure of geometric states into primal building blocks paves the way to distilling the essence of holography for the emergence of a classical bulk spacetime.

A Parallel Fast Multipole Method for a Space-Time Boundary Element Method for the Heat Equation

We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an efficient distributed parallelization with respect to time and with a one-directional communication pattern. On top, we apply a task-based shared memory parallelization and SIMD vectorization. In the numerical tests we observe high efficiencies of our parallelization approach.

Partially pivoted ACA based acceleration of the energetic BEM for time-domain acoustic and elastic waves exterior problems

We consider acoustic and elastic wave propagation problems in 2D unbounded domains, reformulated in terms of space-time Boundary Integral Equations (BIEs). For their numerical solution, we employ a weak formulation related to the energy of the system and we discretize the weak problems by a Galerkin-type Boundary Element Method (BEM): this approach, called Energetic BEM, has revealed accurate and stable even on large time intervals of analysis. In particular, it results that, when standard Lagrangian basis functions are considered, the BEM matrices have Toeplitz lower triangular block structure, where blocks for growing time become fully populated; hence the overall memory cost of the energetic BEM is O(M2N), M and N being the number of the space degrees of freedom and the total number of performed time steps, respectively. This drawback prevents the application of such method to large scale problems. As a possible remedy, we propose a fast technique based on the Adaptive Cross Approximation (ACA). The core of this procedure is the approximation of sufficiently large time blocks of the energetic BEM matrix through the partially pivoted ACA algorithm, which allows to compute only few of the original entries. This leads to reduced assembly time, which for the energetic BEM is generally relevant, coupled with reduced memory storage requirements. Additionally, the consequent acceleration of the matrix/vector multiplication together with a marching on time procedure, leads to remarkable reduction of the computational solution time. The effectiveness of the proposed method is theoretically proved and several numerical results are presented and discussed.

Crossing the boundaries: reimagining innovation and diffusion

Boundaries represent separation and the end of one thing and the beginning of another. The diffusion of innovations represents a transmission of information, personal relationships, creativity and similarities across boundaries. While policy and management innovation and diffusion studies began as an American state policy field, over the last 20 years the studies have expanded to include new frameworks for Chinese, Korean and other countries’ innovation and diffusion studies. Using an expanded range of institutional structures, leadership, and factors that impact innovation and diffusion, these studies embrace more comparative studies of policy diffusion across countries. In this paper, we lay out key topics in organizational and policy innovation studies, and independent variables found to lead to innovation and diffusion. In addition, we argue we should expand the types of variables included in multivariate models to empirically test questions related to which innovations diffuse rapidly or incompletely, why governments adopt innovations, and what barriers and resources are present across types of innovations. We introduce three types of boundaries—space boundaries, time and path dependency boundaries, and actors boundaries that we believe should be more regularly and broadly included in innovation and diffusion studies, and we conclude by defining how these boundaries can be operationalized.

Feynman's space-time view in quantum electrodynamics

The present paper offers a reconstruction of what Feynman calls: “the overall spacetime view”. To provide some background, I will rehearse Feynman’s works on the absorber theory of radiation and on path integrals to emphasize the rejection of the so-called “customary view”. Afterward, I will argue that Feynman’s doctoral thesis was instrumental in developing the idea of enclosing a given quantum system into a spacetime boundary. This will be later applied to the path integral formulation and will play a substantial role in the use of asymptotic states in the theory of positron. It is in this latter work that Feynman uses the expression: “overall spacetime view”, referring to the necessity of looking at all the possible quantum phenomena happening within the spacetime boundary. In the last part of the paper, I analyze how such a view applies to Feynman’s work on quantum electrodynamics and Feynman diagrams.

Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains

We consider wave propagation problems in 2D unbounded isotropic homogeneous elastic media, with rigid boundary conditions. For their solution, we propose and compare two alternative numerical approaches, both obtained by coupling the differential equation with the associated space-time boundary integral equation. The latter is defined on an artificial boundary, chosen to surround the (bounded) exterior computational domain of interest. The integral equation defines a boundary condition which is non-reflecting for incoming and also for outgoing waves.In both approaches, the differential equations are discretized by applying a finite element method combined with the Crank Nicolson time marching scheme, while the discretization of the integral equation is obtained by coupling a time convolution quadrature with a space collocation boundary element method. The construction of the two approaches is described and discussed. Some numerical tests are also presented.