scholarly journals Defining Arrow of Time at The Start of Inflation Using Traditional Cosmology Initially as an Example and Finally Penrose Cyclic Conformal Cosmology with Singular versus Nonsingular Starting Points?

2021 ◽  
Author(s):  
Andrew W Beckwith
Keyword(s):  
Quantum Information ◽  
Initial Conditions ◽  
Axiomatic Approach ◽  
Cosmological Models ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Conformal Cosmology ◽  
Definition Of ◽  
Initial Starting

We first of all define the arrow of time. Definition of the arrow of time will allow choosing different initial starting points. One of the issues we will also discuss is the interconnection be-tween the arrow of time, entropy and quantum information. Seth Lloyd in his 2001 work made a linkage between entropy, bits, and information via an axiomatic approach involving time in-tervals. Our take is a bit more general. We will discuss as well the t’Hooft’s statement as to in-itial conditions and times arrow, and how different cosmological models may influence initial conditions. Spoilers alert, if a nonsingular start to expansion existed, this would provide the most straightforward way to avoid a datum from classical relativity. That is, that in the actual equations of classical GR, there is no reason to have time asymmetry. Time asymmetry is built into initial conditions and we will detail several candidates. The first half of the paper brings up cosmology models and forming the arrow of time. The second is related to entropy itself and the problem of information. .

scholarly journals On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

2010 ◽  
Vol 661 ◽  
pp. 446-481 ◽  
Author(s):  
YUE YANG ◽  
D. I. PULLIN
Keyword(s):  
Incompressible Flows ◽  
Initial Conditions ◽  
Scalar Fields ◽  
Local Geometry ◽  
Optimization Approach ◽  
Vortex Reconnection ◽  
Barotropic Flow ◽  
Lagrangian Surfaces ◽  
Definition Of ◽  
Surface Fields

For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor–Green and Kida–Pelz velocity fields, which, at t = 0, satisfy ω·∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions.

scholarly journals Contribution of the intra- and intermolecular routes in autocatalytic zymogen activation: application to pepsinogen activation.

2006 ◽  
Vol 53 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Ramón Varón ◽  
Matilde E Fuentes ◽  
Manuela García-Moreno ◽  
Francisco Garcìa-Sevilla ◽  
Enrique Arias ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Rate Constants ◽  
Time Course ◽  
Initial Conditions ◽  
Reaction Scheme ◽  
Complete Analysis ◽  
Zymogen Activation ◽  
Relative Contribution ◽  
Starting Point ◽  
Definition Of

Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

Time, direction of

2018 ◽  
Author(s):  
Jos Uffink
Keyword(s):  
Boundary Condition ◽  
General Principle ◽  
Room Temperature ◽  
Hot Water ◽  
Initial Condition ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Time Direction ◽  
James Clerk Maxwell ◽  
Ice Cube

You can pour a tumblerful of water into the sea, but you can never get that same tumblerful of water out again. James Clerk Maxwell gave this as an example of an irreversible process. There are many other homely examples: coffee and milk will mix if stirred, but white coffee does not unmix if stirred in reverse. An ice cube in a glass of hot water will melt, but we never see water at room temperature spontaneously separate into ice and hot water. Physical theories like thermodynamics or hydrodynamics, which codify this type of irreversible phenomenon, do not allow the same kind of behaviour in the forward and backward direction of time. There is thus a striking asymmetry in the two temporal directions. This is usually referred to as the ‘direction of time’ (or ‘time asymmetry’ or ‘anisotropy’ or the ‘arrow of time’). The source of this asymmetry has been sought in various theories of physics, both classical and quantum. Some explanations appeal to some sort of boundary condition, typically an initial condition, which the explanation admits to be, not a law of the theory, but a matter of happenstance. Other explanations advocate some additional general principle about, for example, temporally asymmetric notions of causality or randomness.

scholarly journals Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive?

2020 ◽  
Vol 4 (3) ◽  
pp. 40
Author(s):  
Jocelyn Sabatier
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Initial Conditions ◽  
Fractional Integration ◽  
Current Trend ◽  
Singular Kernels ◽  
Fractional Differential ◽  
Definition Of ◽  
A Current

In the field of fractional calculus and applications, a current trend is to propose non-singular kernels for the definition of new fractional integration and differentiation operators. It was recently claimed that fractional-order derivatives defined by continuous (in the sense of non-singular) kernels are too restrictive. This note shows that this conclusion is wrong as it arises from considering the initial conditions incorrectly in (partial or not) fractional differential equations.

The Topography of Historical Contingency

2012 ◽  
Vol 6 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Rob Inkpen ◽  
Derek Turner
Keyword(s):  
Initial Conditions ◽  
Historical Contingency ◽  
Scaling Effects ◽  
Historical Events ◽  
Change Over Time ◽  
Complex Landscape ◽  
Definition Of ◽  
Further Development ◽  
Over Time

Abstract Starting with Ben-Menahem’s definition of historical contingency as sensitivity to variations in initial conditions, we suggest that historical events and processes can be thought of as forming a complex landscape of contingency and necessity. We suggest three different ways of extending and elaborating Ben-Menahem’s concepts: (1) By supplementing them with a notion of historical disturbance; (2) by pointing out that contingency and necessity are subject to scaling effects; (3) by showing how degrees of contingency/necessity can change over time. We also argue that further development of Sterelny’s notion of conditional inevitability leads to our conclusion that the topography of historical contingency is something that can change over time.

Time symmetric electrodynamics and the arrow of time in cosmology

1964 ◽  
Vol 277 (1368) ◽  
pp. 1-23 ◽  
Keyword(s):  
Refractive Index ◽  
Steady State ◽  
Imaginary Part ◽  
Elementary Theory ◽  
Cosmological Models ◽  
Arrow Of Time ◽  
De Sitter ◽  
Radiative Reaction ◽  
Collisional Damping ◽  
Consistent Solution

This paper seeks to establish a connexion between the local arrow of time given by the electromagnetic radiation and the cosmological arrow of time given by the expansion of the universe. The Wheeler-Feynman absorber theory of radiation is applied to the expanding cosmological models. First, it is shown that the Schwarzschild-Tetrode-Fokker principle of direct interparticle action can be extended to the general Riemannian space-time. This generalization is considerably simplified in the conformally flat spaces—as all the Robertson—Walker spaces are. In the application of the absorber theory to various cosmological models, the refractive index turns out to play a crucial part. The ambiguities connected with the sign of the imaginary part of the refractive index are resolved if two conditions are fulfilled: (i) a search is made for a self-consistent solution with full retarded (or advanced) solutions (ii) in an elementary theory the origin of the imaginary part of the refractive index is traced to the radiative reaction itself and not to the collisional damping considered by Hogarth. It is shown that full retarded solutions are consistent in the steady-state cosmology and full advanced solutions in the Einstein-de Sitter cosmology. Full advanced solutions are not consistent in the former and full retarded solutions in the latter. Some interesting implications of this result in the C -field approach to the steady-state cosmology are considered.

On the dynamics of the Tent function - Phase diagrams

2016 ◽  
Vol 7 (4) ◽  
pp. 261
Author(s):  
Prince Amponsah Kwabi ◽  
William Obeng Denteh ◽  
Richard Kena Boadi
Keyword(s):  
Dynamical Systems ◽  
Phase Diagrams ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Topological Dynamical System ◽  
Topological Transitivity ◽  
Tent Map ◽  
One Dimensional ◽  
Definition Of ◽  
Topological Dynamical Systems

This paper focuses on the study of a one-dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.

scholarly journals ALL UNIVERSES GREAT AND SMALL

2001 ◽  
Vol 10 (06) ◽  
pp. 785-790 ◽  
Author(s):  
JOHN D. BARROW ◽  
HIDEO KODAMA
Keyword(s):  
Compact Space ◽  
Present State ◽  
Initial Conditions ◽  
Cosmological Models ◽  
Topology Of The Universe ◽  
The Universe

If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising from generic initial conditions. We also identify the most general cosmological models with compact space.

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