Thermodynamics in the universe described by the emergence of the space and the energy balance relation

It has previously been shown that it is more general to describe the evolution of the universe based on the emergence of the space and the energy balance relation. Here we investigate the thermodynamic properties of the universe described by such a model. We show that the first law of thermodynamics and the generalized second law of thermodynamics (GSLT) are both satisfied and the weak energy condition are also fulfilled for two typical examples. Finally we examine the physical consistency for the present model.Comment: 9 pages, 2 figure

Fast convergence layout algorithm for drawing graphs in marching-graph

Marching-Graph is a new visualization that integrates the graph metaphor and the spatial metaphor into a single visualization. It provides users with highly interactive maps for accessing the logical structures of information that has the geographical attributes. Instead of presenting known facts onto maps, it provides a mechanism for users to visually analyze and seek unknown knowledge through effective human-map interaction and navigation across different spaces. However, the traditional force-directed layout algorithms are very slow in reaching an equilibrium configuration of forces. They usually spend tens of seconds making the layout of a graph converge. Thus, those force-directed layout algorithms can not satisfy the requirement for drawing a sequence of graphs rapidly, while the users are quickly marching through the geographic regions. This paper proposes a fast convergence layout method that speeds up the interaction time while users are progressively exploring a sequence of graphs through a series of force-directed layouts in Marching-Graph. It essentially combines a radial tree drawing method and a force-directed graph drawing method to achieve the fast convergence of energy minimization

Exploring spatially referenced information through 2D Marching Graph

In this paper, we proposed a new visualization framework called Marching Graph that integrates the graph metaphor and the spatial metaphor into a single visualization. Marching Graph allows users to navigate the spatially referenced relational data across two different visual metaphors. We use a force-directed layout algorithm to draw a sequence of progressive graphs, G1, G 2, ... Gn in a 2D geometric space that present the spatially referenced relational data. Each graph Gi is associated with a particular geographic region Ri presented by the spatial metaphor. We allow the user to "march" through the thematic map by altering the focus region Ri and the display of its corresponding graph Gi → Ri. The use of 2D visual metaphors facilitates the navigation activities and human cognition process significantly