scholarly journals General solution for classical sequential growth dynamics of causal sets

2006 ◽  
Vol 73 (10) ◽  
Author(s):  
Madhavan Varadarajan ◽  
David Rideout
Keyword(s):  
General Solution ◽  
Growth Dynamics ◽  
Causal Sets

scholarly journals Classical sequential growth dynamics for causal sets

1999 ◽  
Vol 61 (2) ◽  
Author(s):  
D. P. Rideout ◽  
R. D. Sorkin
Keyword(s):  
Growth Dynamics ◽  
Causal Sets

scholarly journals If time had no beginning: growth dynamics for past-infinite causal sets

2021 ◽  
Author(s):  
Bruno Valeixo Bento ◽  
Fay Dowker ◽  
Stav Zalel
Keyword(s):  
Physical Properties ◽  
Set Theory ◽  
Growth Dynamics ◽  
Dynamical Models ◽  
Causal Sets ◽  
Physical Constraints ◽  
The Past ◽  
New Framework

Abstract We explore whether the growth dynamics paradigm of Causal Set Theory is compatible with past-infinite causal sets. We modify the Classical Sequential Growth dynamics of Rideout and Sorkin to accommodate growth "into the past" and discuss what form physical constraints such as causality could take in this new framework. We propose convex-suborders as the "observables" or "physical properties" in a theory in which causal sets can be past-infinite and use this proposal to construct a manifestly covariant framework for dynamical models of growth for past-infinite causal sets.

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

Cristal-growth dynamics of n-doped gaAs

1992 ◽  
Vol 50 (2) ◽  
pp. 1544-1545
Author(s):  
Pham V. Huong ◽  
Stéphanie Bouchet ◽  
Jean-Claude Launay
Keyword(s):  
Crystal Growth ◽  
Spatial Resolution ◽  
Epitaxial Layer ◽  
Outer Surface ◽  
Gaas Substrate ◽  
Structural Modification ◽  
Growth Dynamics ◽  
Argon Laser ◽  
High Anisotropy ◽  
Crystal Gaas

Microstructure of epitaxial layers of doped GaAs and its crystal growth dynamics on single crystal GaAs substrate were studied by Raman microspectroscopy with a Dilor OMARS instrument equipped with a 1024 photodiode multichannel detector and a ion-argon laser Spectra-Physics emitting at 514.5 nm.The spatial resolution of this technique, less than 1 μm2, allows the recording of Raman spectra at several spots in function of thickness, from the substrate to the outer deposit, including areas around the interface (Fig.l).The high anisotropy of the LO and TO Raman bands is indicative of the orientation of the epitaxial layer as well as of the structural modification in the deposit and in the substrate at the interface.With Sn doped, the epitaxial layer also presents plasmon in Raman scattering. This fact is already very well known, but we additionally observed that its frequency increases with the thickness of the deposit. For a sample with electron density 1020 cm-3, the plasmon L+ appears at 930 and 790 cm-1 near the outer surface.

Contrasting whisker growth dynamics within the phocid lineage

2020 ◽  
Vol 634 ◽  
pp. 231-236 ◽  
Author(s):  
EA McHuron ◽  
T Williams ◽  
DP Costa ◽  
C Reichmuth
Keyword(s):  
Whisker Growth ◽  
Growth Dynamics

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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