Journal articles on the topic 'Mathematical aspects of general relativity'
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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 9, no. 3 (2012): 2269–333. http://dx.doi.org/10.4171/owr/2012/37.
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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 12, no. 3 (2015): 1867–935. http://dx.doi.org/10.4171/owr/2015/33.
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Cederbaum, Carla, Mihalis Dafermos, James A. Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 18, no. 3 (November 25, 2022): 2157–267. http://dx.doi.org/10.4171/owr/2021/40.
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Seidel, Edward, and Wai-Mo Suen. "NUMERICAL RELATIVITY." International Journal of Modern Physics C 05, no. 02 (April 1994): 181–87. http://dx.doi.org/10.1142/s012918319400012x.
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The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques. A set of tools is developed for determining gauge choices, setting boundary and initial conditions, handling spacetime singularities, etc. As required by the special physical and mathematical properties of general relativity, such techniques are indispensable for the numerical evolutions of spacetime. (3) Coding. The optimal use of parallel processing is crucial for many problems in numerical relativity, due to the intrinsic complexity of the theory. (4) Visualization. Numerical relativity is about the evolutions of 3-dimensional geometric structures. There are special demands on visualization. (5) Interpretation and Understanding. The integration of numerical data in relativity into a consistent physical picture is complicated by gauge and coordinate degrees of freedoms and other difficulties. We give a brief overview of the progress made in these areas.
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Benedetto, Elmo, and Fabiano Feleppa. "Underlining some mathematical and physical aspects about the concept of motion in general relativity." Afrika Matematika 29, no. 3-4 (January 24, 2018): 349–56. http://dx.doi.org/10.1007/s13370-018-0545-9.
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GAMBINI, RODOLFO, and JORGE PULLIN. "CLASSICAL AND QUANTUM GENERAL RELATIVITY: A NEW PARADIGM." International Journal of Modern Physics D 14, no. 12 (December 2005): 2355–60. http://dx.doi.org/10.1142/s0218271805007917.
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We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.
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Lin, De-Hone. "The 2+1-Dimensional Special Relativity." Symmetry 14, no. 11 (November 14, 2022): 2403. http://dx.doi.org/10.3390/sym14112403.
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In the new mathematical description of special relativity in terms of the relativistic velocity space, many physical aspects acquire new geometric meanings. Performing conformal deformations upon the 2-dimensional relativistic velocity space for the (2+1)-dimensional special relativity, we find that these conformal deformations correspond to the generalized Lorentz transformations, which are akin to the ordinary Lorentz transformation, but are morphed by a global rescaling of the polar angle and correspondingly characterized by a topological integral index. The generalized Lorentz transformations keep the two fundamental principles of special relativity intact, suggesting that the indexed generalization may be related to the Bondi–Metzner–Sachs (BMS) group of the asymptotic symmetries of the spacetime metric. Furthermore, we investigate the Doppler effect of light, the Planck photon rocket, and the Thomas precession, affirming that they all remain in the same forms of the standard special relativity under the generalized Lorentz transformation. Additionally, we obtain the general formula of the Thomas precession, which gives a clear geometric meaning from the perspective of the gauge field theory in the relativistic velocity space.
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Kolhe, K. G. "Relativity of Pseudo-Spherical Concept and Hartree-Fock Concept for Condensed Matter." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (August 31, 2022): 1839–41. http://dx.doi.org/10.22214/ijraset.2022.46529.
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Abstract: The function Fn,l (r) ;the radial part of of the pseudo-wave function k (r, , ) is expressed in terms of ion-core electron density, n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and helpful in determining many types of electron densities. The physical and mathematical developments on various aspects such as functional densities have been described. It is further emphasized that Fn,l (r) and Pn,l (r) functions and core electron density at different electronic states of the atom that both the functions posses strong correlationship. Study concludes that the present development resulted into an innovative simpler path in the orientation of condensed matter as well as Mathematical Physics.
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Giulini, Domenico. "Aspects of 3-manifold theory in classical and quantum general relativity." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 86, no. 2 (September 19, 2016): 235–71. http://dx.doi.org/10.1007/s12188-016-0135-4.
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Vulcanov, Dumitru N., and Remus-Ştefan Ş. Boată. "Using Algebraic Computing To Teach General Relativity And Cosmology." Annals of West University of Timisoara - Physics 56, no. 1 (December 1, 2012): 139–44. http://dx.doi.org/10.1515/awutp-2015-0022.
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AbstractThe article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.
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Bean, Rachel, Pedro G. Ferreira, and Andy Taylor. "A new golden age: testing general relativity with cosmology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1957 (December 28, 2011): 4941–46. http://dx.doi.org/10.1098/rsta.2011.0366.
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Gravity drives the evolution of the Universe and is at the heart of its complexity. Einstein's field equations can be used to work out the detailed dynamics of space and time and to calculate the emergence of large-scale structure in the distribution of galaxies and radiation. Over the past few years, it has become clear that cosmological observations can be used not only to constrain different world models within the context of Einstein gravity but also to constrain the theory of gravity itself. In this article, we look at different aspects of this new field in which cosmology is used to test theories of gravity with a wide range of observations.
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Vizgin, Vladimir P. "Albert Einstein’s Epistemic Virtues and Vices." Epistemology & Philosophy of Science 58, no. 4 (2021): 175–95. http://dx.doi.org/10.5840/eps202158468.
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The article is based on the concepts of epistemic virtues and epistemic vices and explores A. Einstein’s contribution to the creation of fundamental physical theories, namely the special theory of relativity and general theory of relativity, as well as to the development of a unified field theory on the basis of the geometric field program, which never led to success. Among the main epistemic virtues that led Einstein to success in the construction of the special theory of relativity are the following: a unique physical intuition based on the method of thought experiment and the need for an experimental justification of space-time concepts; striving for simplicity and elegance of theory; scientific courage, rebelliousness, signifying the readiness to engage in confrontation with scientific conventional dogmas and authorities. In the creation of general theory of relativity, another intellectual virtue was added to these virtues: the belief in the heuristic power of the mathematical aspect of physics. At the same time, he had to overcome his initial underestimation of the H. Minkowski’s four-dimensional concept of space and time, which has manifested in a distinctive flexibility of thinking typical for Einstein in his early years. The creative role of Einstein’s mistakes on the way to general relativity was emphasized. These mistakes were mostly related to the difficulties of harmonizing the mathematical and physical aspects of theory, less so to epistemic vices. The ambivalence of the concept of epistemic virtues, which can be transformed into epistemic vices, is noted. This transformation happened in the second half of Einstein’s life, when he for more than thirty years unsuccessfully tried to build a unified geometric field theory and to find an alternative to quantum mechanics with their probabilistic and Copenhagen interpretation In this case, we can talk about the following epistemic vices: the revaluation of mathematical aspect and underestimation of experimentally – empirical aspect of the theory; adopting the concepts general relativity is based on (continualism, classical causality, geometric nature of fundamental interactions) as fundamental; unprecedented persistence in defending the GFP (geometrical field program), despite its failures, and a certain loss of the flexibility of thinking. A cosmological history that is associated both with the application of GTR (general theory of relativity) to the structure of the Universe, and with the missed possibility of discovering the theory of the expanding Universe is intermediate in relation to Einstein’s epistemic virtues and vices. This opportunity was realized by A.A. Friedmann, who defeated Einstein in the dispute about if the Universe was stationary or nonstationary. In this dispute some of Einstein’s vices were revealed, which Friedman did not have. The connection between epistemic virtues and the methodological principles of physics and also with the “fallibilist” concept of scientific knowledge development has been noted.
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De Falco, Vittorio. "New Approaches to the General Relativistic Poynting-Robertson Effect." Emerging Science Journal 4, no. 3 (June 1, 2020): 214–27. http://dx.doi.org/10.28991/esj-2020-01225.
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Objectives: A systematic study on the general relativistic Poynting-Robertson effect has been developed so far by introducing different complementary approaches, which can be mainly divided in two kinds: (1) improving the theoretical assessments and model in its simple aspects, and (2) extracting mathematical and physical information from such system with the aim to extend methods or results to other similar physical systems of analogue structure. Methods/Analysis: We use these theoretical approaches: relativity of observer splitting formalism; Lagrangian formalism and Rayleigh potential with a new integration method; Lyapunov theory os stability. Findings: We determined the three-dimensional formulation of the general relativistic Poynting-Robertson effect model. We determine the analytical form of the Rayleigh potential and discuss its implications. We prove that the critical hypersurfaces (regions where there is a balance between gravitational and radiation forces) are stable configurations. Novelty/Improvement: Our new contributions are: to have introduced the three-dimensional description; to have determined the general relativistic Rayleigh potential for the first time in the General Relativity literature; to have provided an alternative, general and more elegant proof of the stability of the critical hypersurfaces.
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Aref′eva, I. Ya, A. A. Bagrov, and L. V. Joukovskaya. "Several aspects of applying distributions to analysis of gravitational shock waves in general relativity." St. Petersburg Mathematical Journal 22, no. 3 (June 1, 2011): 337. http://dx.doi.org/10.1090/s1061-0022-2011-01144-6.
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Nandi, Kamal K. "Some Aspects of Minimally Relativistic Newtonian Gravity." Zeitschrift für Naturforschung A 46, no. 12 (December 1, 1991): 1026–32. http://dx.doi.org/10.1515/zna-1991-1205.
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Abstract This paper aims to examine if the classical tests of General Relativity (GR) can be predicted by a simpler approach based on minimal changes in the Newtonian gravity. The approach yields a precession of the perihelion of Mercury by an amount 39.4"/century which is very close to the observed Dicke-Goldenberg value (39.6"/century), but less than the popularly accepted value (43"/ century). The other tests exactly coincide with those of GR. Our analysis also displays the genesis as well as the role of geometry in the description of gravitational processes. The time dependent spherically symmetric equations, which are mathematically interesting, call for a further study. The model also allows unambiguous formulation of conservation laws. On the whole, the paper illustrates the limited extent to which a second rank tensor analogy (nonlinear) with flat background Faraday-Maxwell electrodynamics can be pushed in describing gravitation
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BILLYARD, ANDREW, PAUL S. WESSON, and DIMITRI KALLIGAS. "PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY." International Journal of Modern Physics D 04, no. 05 (October 1995): 639–59. http://dx.doi.org/10.1142/s0218271895000430.
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The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.
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Song, Shi Gang, Xia Xia Hu, Jian Liu, and Jian Ma. "Research of Machine Tool Reconfiguration Based on Reliability." Applied Mechanics and Materials 184-185 (June 2012): 397–401. http://dx.doi.org/10.4028/www.scientific.net/amm.184-185.397.
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To adapt to agile workshop environment, the reliability of reconfiguration machine tool was analyzed, and the mathematical models of reconfiguration machine tools’ reliability guideline was established. By modular design of reconfiguration machine tool, the general idea of machine tool reconfiguration oriented to reliability was presented. The machine tool reconfiguration method based on modularization was researched mostly in such aspects as relativity analysis, module reconfiguration of lacking ability parameter, module reconfiguration of redundancy ability parameter. The method solved the rapidity reconfiguration ability of machine tool in system reconfiguration, utilized availability resource reasonably.
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MYRZAKULOV, R., L. SEBASTIANI, and S. ZERBINI. "SOME ASPECTS OF GENERALIZED MODIFIED GRAVITY MODELS." International Journal of Modern Physics D 22, no. 08 (June 21, 2013): 1330017. http://dx.doi.org/10.1142/s0218271813300176.
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In this paper, we review some general aspects of modified gravity theories, investigating mathematical and physical properties and, more specifically, the feature of viable and realistic models able to reproduce the dark energy (DE) epoch and the early-time inflation. We will discuss the black hole (BH) solutions in generalized theories of gravity: it is of fundamental interest to understand how properties and laws of BHs in General Relativity (GR) can be addressed in the framework of modified theories. In particular, we will discuss the energy issue and the possibility to derive the First Law of thermodynamics from the field equations. Then, in the analysis of cosmological solutions, we will pay particular attention to the occurrence of finite-time future singularities and to the possibility to avoid them in [Formula: see text]-gravity. Furthermore, realistic models of F(R)-gravity will be analyzed in detail. A general feature occurring in matter era will be shown, namely, the high derivatives of Hubble parameter may be influenced by the high frequency oscillation of the DE and some correction term may be required in order to stabilize the theory at high redshift. The inflationary scenario is also carefully analyzed and a unified description of the universe is evolved. In the final part of the work, we will look at the last developments in modified gravity, namely, we will investigate cosmological and BH solutions in a covariant field theory of gravity and we will introduce the extended "teleparallel" F(T)-gravity theories. A nice application to the dark matter (DM) problem will be presented.
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MURDZEK, R. "THE GEOMETRY OF THE TORUS UNIVERSE." International Journal of Modern Physics D 16, no. 04 (April 2007): 681–86. http://dx.doi.org/10.1142/s0218271807009826.
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In this contribution, we show that the cyclic universe models naturally emerge from torus geometry in a braneworld scenario. The Riemannian metric on torus and the fundamental tensors of the General Relativity are derived. A discussion on particular aspects of this model is also given.
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Kouneiher, Joseph, and Cécile Barbachoux. "Cartan's soldered spaces and conservation laws in physics." International Journal of Geometric Methods in Modern Physics 12, no. 09 (October 2015): 1550089. http://dx.doi.org/10.1142/s0219887815500899.
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In this paper, we will introduce a generalized soldering p-forms geometry, which can be the right framework to describe many new approaches and concepts in modern physics. Here we will treat some aspects of the theory of local cohomology in fields theory or more precisely the theory of soldering-form conservation laws in physics. We provide some illustrative applications, primarily taken from the Einstein equations of general theory of relativity and Yang–Mills theory. This theory can be considered to be a generalization of Noether's theory of conserved current to differential forms of any degree. An essential result of this, is that the conservation of the energy–momentum in general relativity, is linked to the fact that the vacuum field equations are equivalent to the integrability conditions of a first-order system of differential equations. We also apply the idea of the soldered space and the integrability conditions to the case of Yang–Mills theory. The mathematical framework, where these intuitive considerations would fit naturally, can be used to describe also the dynamics of changing manifolds.
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Stuckey, W. Mark, Timothy McDevitt, and Michael Silberstein. ""Mysteries" of Modern Physics and the Fundamental Constants c, h, and G." Quanta 11, no. 1 (June 15, 2022): 5–14. http://dx.doi.org/10.12743/quanta.v11i1.189.
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We review how the kinematic structures of special relativity and quantum mechanics both stem from the relativity principle, i.e., "no preferred reference frame" (NPRF). Essentially, NPRF applied to the measurement of the speed of light c gives the light postulate and leads to the geometry of Minkowski space, while NPRF applied to the measurement of Planck's constant h gives "average-only" projection and leads to the denumerable-dimensional Hilbert space of quantum mechanics. These kinematic structures contain the counterintuitive aspects ("mysteries") of time dilation, length contraction, and quantum entanglement. In this essay, we extend the application of NPRF to the gravitational constant G and show that it leads to the "mystery" of the contextuality of mass in general relativity. Thus, we see an underlying coherence and integrity in modern physics via its "mysteries" and the fundamental constants c, h, and G. It is well known that Minkowski and Einstein were greatly influenced by David Hilbert in their development of special relativity and general relativity, respectively, but relating those theories to quantum mechanics via its non-Boolean Hilbert space kinematics is perhaps surprising.Quanta 2022; 11: 5–14.
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Zebua, Samuel, and Edwin Waruwu. "Students' Mathematical Procedural Fluency Based on Self-regulated learning." Journal of Innovation and Research in Primary Education 1, no. 2 (November 17, 2022): 56–62. http://dx.doi.org/10.56916/jirpe.v1i2.179.
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Mathematical procedural fluency is an important aspect and must be mastered by students, whose mathematical skills are built on conceptual understanding, strategic competence, adaptive reasoning, and problem-solving. Procedural skills are also related to attitude aspects such as self-regulated learning. Therefore, this study aims to analyze mathematical procedural fluency based on students' self-regulated learning. The research method used is descriptive qualitative. The subjects in this study involved 10 6th grade students at SDN 075061 Balodano. The data analysis technique was carried out descriptively through analysis text. The description of students' self-regulated learning and its relation to mathematical procedural fluency was also analyzed descriptively through a graphical display of data. The results showed that the general description of students' mathematical procedural fluency was still relatively low. However, in general, students showed a positive attitude towards self-regulated learning. Overall, the results of this study indicate a relationship between mathematical procedural fluency and self-regulated learning.
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Hill, James M., and Barry J. Cox. "Einstein's special relativity beyond the speed of light." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (October 3, 2012): 4174–92. http://dx.doi.org/10.1098/rspa.2012.0340.
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We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c , and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy–momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae and where denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an example having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.
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Et. al., Dr Indrajit Patra ,. "Shifts in the Foundation: The Continual Modification and Generalization of Axioms and the Search for the Mathematical Principles that Underlie our Reality." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 11, 2021): 1095–106. http://dx.doi.org/10.17762/turcomat.v12i2.1126.
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The study shall seek to explore the deep, underlying correspondence between the mathematical world of pure numbers and our physical reality. The study begins by pointing out that while the familiar, one-dimensional real numbers quantify many aspects of our day-to-day reality, complex numbers provide the mathematical foundations of quantum mechanics and also describe the behavior of more complicated quantum networks and multi-party correlations, and quaternions underlie Einsteinian special theory of relativity, and then poses the question whether the octonions could play a similar role in constructing a grander theory of our universe. The study then points out that by increasing the level of abstraction and generalization of axiomatic assumptions, we could construct a more powerful number system based on octonions, the seditions, or even other hypercomplex numbers so that we may more accurately describe the universe in its totality.
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Riazuelo, Alain. "Seeing relativity-I: Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars." International Journal of Modern Physics D 28, no. 02 (January 2019): 1950042. http://dx.doi.org/10.1142/s0218271819500421.
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We present an implementation of a ray tracing code in the Schwarzschild metric. We aim at building a numerical code with a correct implementation of both special (aberration, amplification and Doppler) and general (deflection of light, lensing and gravitational redshift) relativistic effects so as to simulate what an observer with arbitrary velocity would see near, or possibly within, the black hole. We also pay some specific attention to perform a satisfactory rendering of stars. Using this code, we then show several unexplored features of the maximal analytical extension of the metric. In particular, we study the aspect of the second asymptotic region of the metric as seen by an observer crossing the horizon. We also address several aspects related to the white hole region (i.e. past singularity) seen both from outside the black hole, inside the future horizon and inside the past horizon, which gives rise to the most counter-intuitive effects.
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Rubiera-Garcia, Diego. "From fundamental physics to tests with compact objects in metric-affine theories of gravity." International Journal of Modern Physics D 29, no. 11 (May 26, 2020): 2041007. http://dx.doi.org/10.1142/s0218271820410072.
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This paper provides a short but comprehensible overview of some relevant aspects of metric-affine theories of gravity in relation to the physics and astrophysics of compact objects. We shall highlight the pertinence of this approach to supersede General Relativity on its strong-field regime, as well as its advantages and some of its difficulties. Moreover, we shall reflect on the present and future opportunities to test its predictions with relativistic and nonrelativistic stars, black holes, and other exotic horizonless compact objects.
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MASHHOON, BAHRAM. "BEYOND GRAVITOELECTROMAGNETISM: CRITICAL SPEED IN GRAVITATIONAL MOTION." International Journal of Modern Physics D 14, no. 12 (December 2005): 2025–37. http://dx.doi.org/10.1142/s0218271805008121.
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A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity is due to the existence of a critical speed. The dynamics of particles moving faster than the critical speed could then be contrary to Newtonian expectations. Working within the framework of gravitoelectromagnetism, the implications of the existence of a critical speed are explored. The results are expected to be significant for high energy astrophysics.
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Belinchón, José Antonio, and Rafael Uribe. "A comparative study of some cosmological models with time varying G and Λ: A symmetry approach." Canadian Journal of Physics 97, no. 10 (October 2019): 1083–95. http://dx.doi.org/10.1139/cjp-2018-0842.
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We study how the constants G and Λ may vary in four different theoretical models: general relativity with time-varying constants (Y.-K. Lau. Aust. J. Phys. 38, 547 (1985). doi: 10.1071/PH850547 ), the model proposed by Lu et al. (Phys Rev D, 89, 063526 (2014). doi: 10.1103/PhysRevD.89.063526 ), the model proposed by Bonanno et al. (Class. Quant. Grav. 24, 1443 (2007). doi: 10.1088/0264-9381/24/6/005 ), and the Brans–Dicke model with Λ([Formula: see text]) [ 25 ]. To carry out this study, we work under the self-similar hypothesis and we assume the same metric, a flat Friedmann–Robertson–Walker metric, and the same matter source, a perfect fluid. We put special emphasis on mathematical and formal aspects, which allows us to calculate exact power-law solutions through symmetry methods, matter collineation, and Noether symmetries. This enables us to compare the solutions of each model and in the same way to contrast the results with some observational data.
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Kholid, Muhammad Noor, and Mardiana Nissa. "Students' Math Literacy in Solving PISA-Like Problems in Papuan Local Context." AL-ISHLAH: Jurnal Pendidikan 14, no. 4 (September 19, 2022): 5645–56. http://dx.doi.org/10.35445/alishlah.v14i4.2258.
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Mathematical literacy in Indonesia is still relatively low. Student achievement in PISA questions is also still not adequate. Mathematical literacy is not limited to the ability to apply quantitative aspects of mathematics, it employs knowledge of mathematics in a broad sense. Mathematical literacy skills are closely related to interpreting problems related to local contexts into mathematical problems. This study aims to describe students' mathematical literacy activities in solving problems similar to PISA in the regional context; the context in which this research is desired is the local Papuan context. The research method employed is the descriptive qualitative method. The samples were 8th graders of SMP Batik Program Khusus Kartasura, totaling six students. Data was collected using a written test consisting of two items of PISA-like problems, observations, and interviews. This research produces problems similar to PISA within the local context of Papua. PISA-like questions are declared to be valid, simple, and have the potential to determine students' mathematical literacy abilities. The PISA-like problems are valid based on the review by experts in the appropriate field in terms of aspects, content, structure, and language. This PISA-like problem was also developed based on seven basic mathematical abilities that employ mathematical literacy. We successfully concluded that the dominant aspects for students are making assumptions and conceptualizing. While the parts of structuring and formulating a model are not dominant. In addition, PISA-like problems have more potential effect on determining students' mathematical literacy.
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NI, WEI-TOU. "EMPIRICAL FOUNDATIONS OF THE RELATIVISTIC GRAVITY." International Journal of Modern Physics D 14, no. 06 (June 2005): 901–21. http://dx.doi.org/10.1142/s0218271805007139.
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In 1859, Le Verrier discovered the mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 141 years to 2000, the precisions of laboratory and space experiments, and astrophysical and cosmological observations on relativistic gravity have been improved by 3 orders of magnitude. In 1999, we envisaged a 3–6 order improvement in the next 30 years in all directions of tests of relativistic gravity. In 2000, the interferometric gravitational wave detectors began their runs to accumulate data. In 2003, the measurement of relativistic Shapiro time-delay of the Cassini spacecraft determined the relativistic-gravity parameter γ to be 1.000021 ± 0.000023 of general relativity — a 1.5-order improvement. In October 2004, Ciufolini and Pavlis reported a measurement of the Lense–Thirring effect on the LAGEOS and LAGEOS2 satellites to be 0.99 ± 0.10 of the value predicted by general relativity. In April 2004, Gravity Probe B (Stanford relativity gyroscope experiment to measure the Lense–Thirring effect to 1%) was launched and has been accumulating science data for more than 170 days now. μSCOPE (MICROSCOPE: MICRO-Satellite à trainée Compensée pour l'Observation du Principle d'Équivalence) is on its way for a 2008 launch to test Galileo equivalence principle to 10-15. LISA Pathfinder (SMART2), the technological demonstrator for the LISA (Laser Interferometer Space Antenna) mission is well on its way for a 2009 launch. STEP (Satellite Test of Equivalence Principle), and ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) are in good planning stage. Various astrophysical tests and cosmological tests of relativistic gravity will reach precision and ultra-precision stages. Clock tests and atomic interferometry tests of relativistic gravity will reach an ever-increasing precision. These will give revived interest and development both in experimental and theoretical aspects of gravity, and may lead to answers to some profound questions of gravity and the cosmos.
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Romenski, E., I. Peshkov, M. Dumbser, and F. Fambri. "A new continuum model for general relativistic viscous heat-conducting media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (March 30, 2020): 20190175. http://dx.doi.org/10.1098/rsta.2019.0175.
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The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein’s special relativity and the Euler–Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.
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Curcio, Luciano, Laura D'Orsi, and Andrea De Gaetano. "Seven Mathematical Models of Hemorrhagic Shock." Computational and Mathematical Methods in Medicine 2021 (June 3, 2021): 1–34. http://dx.doi.org/10.1155/2021/6640638.
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Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject’s responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.
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Sun, Haojie, Xun Zhou, Yanyun Meng, and Zezhong Yang. "Research on the Cognition Degree of Mathematical Operation Literacy by Pre-service High School Mathematics Teachers." International Academic Journal of Education and Literature 3, no. 02 (April 30, 2022): 17–27. http://dx.doi.org/10.47310/iajel.2022.v03i02.003.
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At present, mathematical operation literacy has generated extensive attention from all walks of life, many questions about it have been studied except the cognition of pre-service high school mathematics teachers on mathematical operation literacy. To address this gap, This study analyzed the cognition degree of mathematical operation literacy of 51 pre-service high school mathematics teachers with an open-ended questionnaire self-designed. After analyzing, it could be found that: a. The scope of cognition is not very broad, about 40% of the content is not recognized, and the communication and reflection aspect is unrecognized; b. Their cognition is not deep, their cognitive level mainly stays at level 1. Their cognition is not continuous and linear; c. A few aspects of cognition are relatively clear, but in general, their cognition is not very clear. The content that they can clearly recognize is mainly the definition and expression of mathematical operation literacy and the aspect of knowledge and skill. Therefore, it is suggested that: a. Experts and teachers in charge of certification work should expand mathematical operation literacy courses and pay more attention to them; b. Pre-service teachers should fully understand the related contents of mathematical operation literacy, go deep into each level, and clarify the expression of mathematical operation literacy. Contribution/Originality: This study analyzed the cognition degree of mathematical operation literacy of current pre-service high school mathematics teachers in China with an open-ended questionnaire self-designed. The results are conducive to reforming the present Chinese teaching and curriculum in order to improve the training for pre-service teachers.
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Leonhardt, Ulf, and Thomas G. Philbin. "The case for artificial black holes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1877 (June 5, 2008): 2851–57. http://dx.doi.org/10.1098/rsta.2008.0072.
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The event horizon is predicted to generate particles from the quantum vacuum, an effect that bridges three areas of physics—general relativity, quantum mechanics and thermodynamics. The quantum radiation of real black holes is too feeble to be detectable, but black-hole analogues may probe several aspects of quantum black holes. In this paper, we explain in simple terms some of the motivations behind the study of artificial black holes.
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Karjiyati, Victoria, Irfan Supriatna, Neza Agusdianita, and Nani Yuliantini. "Peningkatan Kemampuan Literasi Matematika Mahasiswa Melalui Penerapan Model RME Pada Perkuliahan Konsep Dasar Geometri dan Pengukuran." Jurnal PGSD: Jurnal Ilmiah Pendidikan Guru Sekolah Dasar 15, no. 1 (May 31, 2022): 49–56. http://dx.doi.org/10.33369/pgsd.15.1.49-56.
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Education in Indonesia is currently promoting literacy education. One of the highlights is mathematical literacy. Mathematical literacy ability in Indonesia is still relatively low. This is evidenced by the results of the 2018 Program for International Assessment (PISA) survey, in the field of mathematics, Indonesia is ranked 72 out of 78 countries with a score of 379. The objectives of the research are: to improve students' mathematical literacy skills in the Basic Concepts of geometry and measurement lectures in PGSD FKIP Study Program, Bengkulu University by applying a realistic mathematics education (RME) model. This research uses action research method (Action Research). Data collection techniques aspects of the management of the learning process will collect data in the form of information through observation, and tests of mathematical literacy skills then summarized and described in the form of a data matrix. Data were analyzed through qualitative descriptive. The results of the study have been carried out in lectures by applying the RME model in the Basic Concepts of Geometry and Measurement course. Students' mathematical literacy test results also increased. The highest increase in the aspect of context literacy.
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Gupta, Rohit K., Supriya Kar, and R. Nitish. "Aspects of gravitational wave/particle duality: Bulk torsion ↔boundary gravity correspondence." International Journal of Modern Physics D 29, no. 02 (January 2020): 2050019. http://dx.doi.org/10.1142/s0218271820500194.
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A geometric torsion (GT) underlying a [Formula: see text]-form in a [Formula: see text]-dimensional [Formula: see text] gauge theory is revisited with a renewed perspective for a nonperturbation (NP) gravity in [Formula: see text]. In this context, we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a [Formula: see text] coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is identified as a mass dipole and is shown to be sourced by a propagating GT. A detailed analysis is performed in a bulk GT to show a modification to the precession of perihelion in a boundary NP gravity. The perspective of an electromagnetic (EM) wave in the bulk is investigated to reveal a spin [Formula: see text] (mass-less) quantum sourced by an apparent 2-form. A Goldstone scalar is absorbed by the apparent 2-form to describe a massive [Formula: see text]-form in the coulomb gauge. Alternately a Goldstone scalar together with a local degree of GT and 2-form is argued to govern a composite (mass-less) spin [Formula: see text] particle in Lorentz gauge. Both the scenarios, further ensure a graviton in a boundary NP gravity. A qualitative analysis reveals a (noninteracting) graviton underlying a plausible gravitational wave/particle duality in NP gravity.
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Scholz, Erhard. "Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures." Science in Context 17, no. 1-2 (June 2004): 165–97. http://dx.doi.org/10.1017/s0269889704000080.
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Hermann Weyl (1885–1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a “purely infinitesimal” aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations.
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Brumberg, V. A., J. Henrard, Ju V. Batrakov, K. B. Bhatnagar, J. Chapront, A. Deprit, S. Ferraz-Mello, et al. "7 - Mecanique Celeste (Celestial Mechanics)." Transactions of the International Astronomical Union 20, no. 1 (1988): 15–28. http://dx.doi.org/10.1017/s0251107x0000688x.
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During 1985-1987 Celestial Mechanics has been intensively developed in all its branches embracing physical bases, mathematical aspects, computational techniques and astronomical objectives. Commission 7 has organized three IAU conferences: Symposium No. 114 “Relativity in Celestial Mechanics and Astrometry” (Leningrad, May 1985), Colloquium No. 96 “The Few Body Problem” (Turku, June 1987) and Topical Session “Resonances in the Solar System” of the X-th European Regional Astronomy Meeting (Prague, August 1987). Members of the commission have broadly participated in the NATO Advanced Study Institute “Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems” (Cortina d’Ampezzo, August 1987) and some other international and regional conferences. Prospects of the actual celestial mechanics investigations have been discussed at a session of Commission 7 at the XIX-th IAU General Assembly (New Delhi, November 1985). Three papers dealing with the unsolved problems of celestial mechanics were primarily addressed to the rising generation of celestial mechanicians (V. A. Brumberg and J. Kovalevsky, CM. 39, 133, 1986; P.K. Seidelmann, CM. 39, 141, 1986).
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Lalli, Roberto. "‘Dirty work’, but someone has to do it: Howard P. Robertson and the refereeing practices of Physical Review in the 1930s." Notes and Records: the Royal Society Journal of the History of Science 70, no. 2 (January 27, 2016): 151–74. http://dx.doi.org/10.1098/rsnr.2015.0022.
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In the 1930s the mathematical physicist Howard P. Robertson was the main referee of the journal Physical Review for papers concerning general relativity and related subjects. The rich correspondence between Robertson and the editors of the journal enables a historical investigation of the refereeing process of Physical Review at the time that it was becoming one of the most influential physics periodicals in the world. By focusing on this case study, the paper investigates two complementary aspects of the evolution of the refereeing process: first, the historical evolution of the refereeing practices in connection with broader contextual changes, and second, the attempts to define the activity of the referee, including the epistemic virtues required and the journal's functions according to the participants' categories. By exploring the tension between Robertson's idealized picture about how the referee should behave and the desire to promote his intellectual agenda, I show that the evaluation criteria that Robertson employed were contextually dependent and I argue that, in the 1930s, through his reports the referee had an enormous power in defining what direction future research should take.
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Beltrán Jiménez, Jose, Lavinia Heisenberg, and Tomi S. Koivisto. "The canonical frame of purified gravity." International Journal of Modern Physics D 28, no. 14 (October 2019): 1944012. http://dx.doi.org/10.1142/s0218271819440127.
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In the recently introduced gauge theory of translations, dubbed Coincident General Relativity (CGR), gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry and avoids the second derivatives that appear in the conventional Einstein–Hilbert action. While it implies the equivalent classical dynamics, the improved action principle can make a difference in considerations of energetics, thermodynamics and quantum theory. This paper reports on possible progress in those three aspects of gravity theory. In the so-called purified gravity, (1) energy–momentum is described locally by a conserved, symmetric tensor, (2) the Euclidean path integral is convergent without the addition of boundary or regulating terms and (3) it is possible to identify a canonical frame for quantization.
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Zhu, Ben-Chao, and Xiang-Song Chen. "Tensor gauge condition and tensor field decomposition." Modern Physics Letters A 30, no. 35 (October 28, 2015): 1550192. http://dx.doi.org/10.1142/s0217732315501928.
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We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin [Formula: see text]. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
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RUFFINI, REMO, C. R. ARGÜELLES, B. M. O. FRAGA, A. GERALICO, H. QUEVEDO, J. A. RUEDA, and I. SIUTSOU. "BLACK HOLES IN GAMMA RAY BURSTS AND GALACTIC NUCLEI." International Journal of Modern Physics D 22, no. 11 (September 2013): 1360008. http://dx.doi.org/10.1142/s0218271813600080.
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Current research marks a clear success in identifying the moment of formation of a Black Hole of ~ 10M⊙, with the emission of a Gamma Ray Burst. This explains in terms of the 'Blackholic Energy' the source of the energy of these astrophysical systems. Their energetics up to 1054 erg, make them detectable all over our Universe. Concurrently a new problematic has been arising related to: (a) The evidence of Dark Matter in galactic halos; (b) The origin of the Super Massive Black Holes in active galactic nuclei and Quasars and (c) The purported existence of a Black Hole in the Center of our Galaxy. These three aspects of this new problematic have been traditionally approached independently. We propose an unified approach to all three of them based on a system of massive self-gravitating neutrinos in General Relativity. Perspectives of future research are presented.
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Pacini, Giovanni, Bo Ahrén, Christian Göbl, and Andrea Tura. "Assessing the Effect of Incretin Hormones and Other Insulin Secretagogues on Pancreatic Beta-Cell Function: Review on Mathematical Modelling Approaches." Biomedicines 10, no. 5 (May 3, 2022): 1060. http://dx.doi.org/10.3390/biomedicines10051060.
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Mathematical modelling in glucose metabolism has proven very useful for different reasons. Several models have allowed deeper understanding of the relevant physiological and pathophysiological aspects and promoted new experimental activity to reach increased knowledge of the biological and physiological systems of interest. Glucose metabolism modelling has also proven useful to identify the parameters with specific physiological meaning in single individuals, this being relevant for clinical applications in terms of precision diagnostics or therapy. Among those model-based physiological parameters, an important role resides in those for the assessment of different functional aspects of the pancreatic beta cell. This study focuses on the mathematical models of incretin hormones and other endogenous substances with known effects on insulin secretion and beta-cell function, mainly amino acids, non-esterified fatty acids, and glucagon. We found that there is a relatively large number of mathematical models for the effects on the beta cells of incretin hormones, both at the cellular/organ level or at the higher, whole-body level. In contrast, very few models were identified for the assessment of the effect of other insulin secretagogues. Given the opportunities offered by mathematical modelling, we believe that novel models in the investigated field are certainly advisable.
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Cadoni, Mariano, Matteo Tuveri, and Andrea P. Sanna. "Long-Range Quantum Gravity." Symmetry 12, no. 9 (August 21, 2020): 1396. http://dx.doi.org/10.3390/sym12091396.
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It is a tantalising possibility that quantum gravity (QG) states remaining coherent at astrophysical, galactic and cosmological scales could exist and that they could play a crucial role in understanding macroscopic gravitational effects. We explore, using only general principles of General Relativity, quantum and statistical mechanics, the possibility of using long-range QG states to describe black holes. In particular, we discuss in a critical way the interplay between various aspects of long-range quantum gravity, such as the holographic bound, classical and quantum criticality and the recently proposed quantum thermal generalisation of Einstein’s equivalence principle. We also show how black hole thermodynamics can be easily explained in this framework.
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Pilarczyk, K. W. "DESIGN ASPECTS OF BLOCK REVETMENTS." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 151. http://dx.doi.org/10.9753/icce.v21.151.
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The increasing shortage and costs of natural materials in certain geographical areas has resulted in recent years, inter alia, in the rapid development of artificial (concrete) block revetments. In general, two main types of revetments can be distinguished: permeable (stone pitching, placed relatively open block-mats) and (relatively-) impermeable (closed blocks, concrete slabs). Regarding the shape and/or placing technique a distinction can be made between: a) free (mostly rectangular-) blocks and b) interlocking blocks of different design (tongue-and-groove connection, ship- lap, cabling, blocks connected to geotextile by pins etc.). In all these cases the type of sublayer (permeable/impermeable) and the grade of permeability of the toplayer are very important factors in the stability of these revetments. The design also needs to be made (executed) and maintained. Both aspects must therefore already be taken along within the stadium of designing. At the moment there is a large variety of types of revetment-blocks and other defence systems (i.e. block-mats), see Fig. 1. Until recently no objective design-criteria were available for most types/systems of blocks. The choice (type and size) of the revetments built sofar is only based on experience and on personal points of view, sometimes supported by small-scale model investigations. In the light of new (stricter) rules regarding the safety of the Dutch dikes, as they have been drawn up by the Delta-Commission, the need for proper design-criteria for the revetments of dikes has evidently grown. Because of the complexity of the problem no simply, generally valid mathematical model for the stability of the revetment are available yet. For restricted areas of application however, fairly reliable criteria (often supported by large-scale tests) have been developed in the Netherlands not only for the kind of revetment, but also for conditions of loads. This new approach is discussed in (Klein Breteler, 1988). This paper presents a short state-of-the-art review of existing knowledge on the designing of different types of revetments and, where ever possible, the available stability criteria are mentioned. There is also given some comparison of the different types of revetments with their advantages and disadvantages and suggestions regarding their practical application.
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BARCELÓ, CARLOS, STEFANO LIBERATI, and MATT VISSER. "ANALOGUE MODELS FOR FRW COSMOLOGIES." International Journal of Modern Physics D 12, no. 09 (October 2003): 1641–49. http://dx.doi.org/10.1142/s0218271803004092.
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It is by now well known that various condensed matter systems may be used to mimic many of the kinematic aspects of general relativity, and in particular of curved-spacetime quantum field theory. In this essay we will take a look at what would be needed to mimic a cosmological spacetime — to be precise a spatially flat FRW cosmology — in one of these analogue models. In order to do this one needs to build and control suitable time dependent systems. We discuss here two quite different ways to achieve this goal. One might rely on an explosion, physically mimicking the big bang by an outflow of whatever medium is being used to carry the excitations of the analogue model, but this idea appears to encounter dynamical problems in practice. More subtly, one can avoid the need for any actual physical motion (and avoid the dynamical problems) by instead adjusting the propagation speed of the excitations of the analogue model. We shall focus on this more promising route and discuss its practicality.
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Et. al., Dr Indrajit Patra,. "Do They Compute? Dawn of a New Paradigm based on the Information-theoretic View of Black holes, Universe and Various Conceptual Interconnections of Fundamental Physics." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 11, 2021): 1208–21. http://dx.doi.org/10.17762/turcomat.v12i2.1145.
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The article endeavors to show how thinking about black holes as some form of hyper-efficient, serial computers could help us in thinking about the more fundamental aspects of space-time itself. Black holes as the most exotic and yet simplest forms of gravitational systems also embody quantum fluctuations that could be manipulated to archive hypercomputation, and even if this approach might not be realistic, yet it is important since it has deep connections with various aspects of quantum gravity, the highly desired unification of quantum mechanics and general relativity. The article describes how thinking about black holes as the most efficient kind of computers in the physical universe also paves the way for developing new ideas about such issues as black hole information paradox, the possibility of emulating the properties of curved space-time with the collective quantum behaviors of certain kind of condensate fluids, ideas of holographic spacetime, gravitational thermodynamics and entropic gravity, the role of quantum entanglements and non-locality in the construction of spacetime, spacetime geometry and the nature of gravitation and dark energy and dark matter, etc. to name a few.
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ANDERSON, EDWARD. "RELATIONAL QUADRILATERALLAND I: THE CLASSICAL THEORY." International Journal of Modern Physics D 23, no. 02 (January 29, 2014): 1450014. http://dx.doi.org/10.1142/s021827181450014x.
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Relational particle mechanics models bolster the relational side of the absolute versus relational motion debate. They are additionally toy models for the dynamical formulation of general relativity (GR) and its problem of time (PoT). They cover two aspects that the more commonly studied minisuperspace GR models do not: (1) by having a nontrivial notion of structure and thus of cosmological structure formation and of localized records. (2) They have linear as well as quadratic constraints, which is crucial as regards modeling many PoT facets. I previously solved relational triangleland classically, quantum mechanically and as regards a local resolution of the PoT. This rested on triangleland's shape space being 𝕊2with isometry group SO(3), allowing for use of widely-known geometry, methods and atomic/molecular physics analogies. I now extend this work to the relational quadrilateral, which is far more typical of the general N-a-gon, represents a "diagonal to nondiagonal Bianchi IX minisuperspace" step-up in complexity, and encodes further PoT subtleties. The shape space now being ℂℙ2with isometry group SU(3)/ℤ3, I now need to draw on geometry, shape statistics and particle physics to solve this model; this is therefore an interdisciplinary paper. This Paper treats quadrilateralland at the classical level, and then paper II provides a quantum treatment.
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Linder, Eric V. "Model-independent tests of cosmic gravity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1957 (December 28, 2011): 4985–97. http://dx.doi.org/10.1098/rsta.2011.0288.
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Gravitation governs the expansion and fate of the universe, and the growth of large-scale structure within it, but has not been tested in detail on these cosmic scales. The observed acceleration of the expansion may provide signs of gravitational laws beyond general relativity (GR). Since the form of any such extension is not clear, from either theory or data, we adopt a model-independent approach to parametrizing deviations to the Einstein framework. We explore the phase space dynamics of two key post-GR functions and derive a classification scheme, and an absolute criterion on accuracy necessary for distinguishing classes of gravity models. Future surveys will be able to constrain the post-GR functions' amplitudes and forms to the required precision, and hence reveal new aspects of gravitation.
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AMELINO-CAMELIA, GIOVANNI. "KINEMATICAL SOLUTION OF THE UHE-COSMIC-RAY PUZZLE WITHOUT A PREFERRED CLASS OF INERTIAL OBSERVERS." International Journal of Modern Physics D 12, no. 07 (August 2003): 1211–26. http://dx.doi.org/10.1142/s0218271803003645.
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Among the possible explanations for the puzzling observations of cosmic rays above the GZK cutoff there is growing interest in the ones that represent kinematical solutions, based either on general formulations of particle physics with small violations of Lorentz symmetry or on a quantum-gravity-motivated scheme for the breakdown of Lorentz symmetry. An unappealing aspect of these cosmic-ray-puzzle solutions is that they require the existence of a preferred class of inertial observers. Here I propose a new kinematical solution of the cosmic-ray puzzle, which does not require the existence of a preferred class of inertial observers. My proposal is a new example of a type of relativistic theories, the so-called "doubly-special-relativity" theories, which have already been studied extensively over the last two years. The core ingredient of the proposal is a deformation of Lorentz transformations in which also the Planck scale Ep (in addition to the speed-of-light scale c) is described as an invariant. Just like the introduction of the invariant c requires a deformation of the Galileian transformations into the Lorentz transformations, the introduction of the invariant Ep requires a deformation of the Lorentz transformations, but there is no special class of inertial observers. The Pierre Auger Observatory and the GLAST space telescope should play a key role in future developments of these investigations. I also emphasize that the doubly-special-relativity theory here proposed, besides providing a solution for the cosmic-ray puzzle, is also the first doubly-special-relativity theory with a natural description of macroscopic bodies, and may find applications in the context of a recently-proposed dark-energy scenario.