One-dimensional Universe Research Articles

Mallarmé et le livre-fétiche (Variations sur un sujet)

Abstract: The aim of the present article is to examine a few “variations” on Mallarmé’s idea of the “Livre”: not from the point of view of his “rêve” as expressed in his letter to Verlaine, but through some more concrete examples. These include the still life book, which seems to take inspiration from painters in Divagations ; the book in the prosaic format of the fashion magazine; the illustrated book or artist’s book; the book-object; and the typographic poem, as projected by Un coup de dés . Added to these various material avatars of the ideal “Livre,” I propose the notion of the “livrefétiche,” which preserves the Book’s sacred dimension, while inscribing it in the one-dimensional universe of things: as an anthropological enigma through which the poem questions the human condition. (in French)

On the wave nature of particles

The main goal of the present article is to elucidate the wave-particle duality problem by giving an unambiguous mathematical expression of the origin of the wave nature of particles. It is indicated that the wave nature of particles is originated from the multidimensional universe approach and under the one-dimensional universe assumption the wave nature vanishes. The one-dimensional universe assumption also gives a deterministic explanation for the double-slit experiment and answers how a single electron can interfere with itself. The locality paradox is also discussed. It is demonstrated that the same principle shows how a local measurement can determine the state of a distant system. The theoretical framework presented here may help us to understand various quantum physics phenomena. i.e., the superposition principle, wave function collapse, and entanglement.

One-dimensional Toy Cosmological Model

In this work, we explore a one-dimensional universe, a toy model based on the relativistic particle theory, seen as a one-dimensional field theory coupled to gravity. The gravitational field is represented by an einbein. Working in a cosmological context, we suppose as gravitational sources a set of scalar fields, and invoking ideas from finite temperature field theory, we find that under certain assumptions this toy model leads to regimes similar to inflation.

Cantorian-Fractal Kinetic Energy and Potential Energy as the Ordinary and Dark Energy Density of the Cosmos Respectively

In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.

Can a Species Keep Pace with a Shifting Climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back.

Heap-based algorithm and one-dimensional expanding Universe

A fast algorithm for studying one-dimensional systems that are Lagrangian integrable between collisions is presented. The algorithm is based on an event-driven scheme, and uses a heap ordered set of predicted future events. As an application, we discuss the case of an expanding one-dimensional Universe.

Self-Attracting Poisson Clouds in an Expanding Universe

We consider the following elementary model for clustering by ballistic aggregation in an expanding universe. At the initial time, there is a doubly infinite sequence of particles lying in a one-dimensional universe that is expanding at constant rate. We suppose that each particle p attracts points at a certain rate a(p)/2 depending only on p, and when two particles, say p and q, collide by the effect of attraction, they merge as a single particle p*q. The main purpose of this work is to point at the following remarkable property of Poisson clouds in these dynamics. Under certain technical conditions, if at the initial time the system is distributed according to a spatially stationary Poisson cloud with intensity μ0, then at any time t > 0, the system will again have a Poissonian distribution, now with intensity μt, where the family \(\) solves a generalization of Smoluchowski's coagulation equation.

Evolution of the Power Spectrum and Self‐Similarity in the Expanding One‐dimensional Universe

We have investigated time evolutions of power spectra of density fluctuations for a long time after the first appearance of caustics in the expanding one-dimensional universe. It is found that when an initial power spectrum is scale-free with a power index n, self-similarity of the time evolution of the power spectrum is achieved. We find that the power spectrum can be separated roughly into three regimes according to the shape of the power spectrum: the linear regime (k ksnl: regime 3). The power index of the power spectrum in each regime has values of n, -1, and μ, respectively, which depend on n. Even in the case of an initial power-law spectrum with a cutoff scale, there might be the possibility of self-similar evolution of the power spectrum after the appearance of the caustics. It is found, however, that self-similarity is not achieved in this case. The shape of the power spectrum on scales smaller than the cutoff scale can be separated roughly into two regimes: the virialized regime (kcut kcs: regime 5). The power index of the power spectrum is ν, which may be determined by the distribution of singular points in regime 4. In regime 5, the value of the power index is -1. Moreover, we show the general property of the shape of a power spectrum with a general initial condition.

An automaton analogue of unicellularity

There is presented in outline form an abstract model of a cell in an evolutionary context. The design is based on an elaboration of John Holland's one-dimensional, abstract universe recently posed for the study of the emergence of self-replicating systems. Eight new ingredients constitute the elaboration. They suggest how compartmentation of a set of “molecules” in a one-dimensional universe can be achieved and how a suitable, compartmentalized set of molecules can replicate in a manner analogous to real cell replication, i.e., there is segregation and semi-conservative replication of the genetic material, and there is division of the compartment through the construction of an “inner membrane”. The approach to self-replication of a spatially delimited entity exemplified by this design differs from the abstract models of replication of the von Neumann or Laing type. In these the replicating entity constructs a copy external to itself and does not undergo any essential replacement of any of its own parts. Also, while in these models the concern is primarily with questions of the “logical” type, our design has in mind features identifiable with both energy and information considerations. Thus, the rules which define the underlying “physics and chemistry” imply that the self-replicating entity is a dissipative structure. A constant flux of energy is required to maintain the system far from thermodynamic equilibrium in order to account for multiple steady states, and hence dynamic structure.