Thermodynamics of Quantum Ultra-cold Neutron Gas under Gravity of The Earth

The stored ultra-cold neutrons have been developed. A high density ultra-cold neutron gas has been recently produced by using the nuclear spallation method. We investigate the thermodynamic properties of the quantum ultra-cold neutron gas in the Earth's gravitational field. We find that the quantum effects increase temperature dependence of the chemical potential and the internal energy in the low temperature region. The density distribution of quantum ultra-cold neutron gas is modified by the Earth's gravitational field.Comment: 7 pages, 4 figures, Submitted to Progress of Theoretical Physic

A necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two

AbstractA P⩾3-factor F of a graph G is a spanning subgraph of G such that every component of F is a path of length at least two. Let R be a factor-critical graph with at least three vertices, that is, for each x∈V(R),R−x has a 1-factor (i.e., a perfect matching). Set V(R)={x1,…,xn}. Add new vertices {v1,…,vn} to R together with the edges xivi,1⩽i⩽n. The resulting graph H is called a sun. (Note that degHvi=1 for all i,1⩽i⩽n.) K1 and K2, i.e., the complete graphs with one and two vertices, respectively, are also called suns. Then let C be the set of all suns. A sun component of a graph is a component which belongs to C. Let cs(G) denote the number of sun components of G. We prove that a graph G has a P⩾3-factor if and only if cs(G−S)⩽2|S|, for every subset S of V(G)

Horizontal transfer between loose compartments stabilizes replication of fragmented ribozymes

The emergence of replicases that can replicate themselves is a central issue in the origin of life. Recent experiments suggest that such replicases can be realized if an RNA polymerase ribozyme is divided into fragments short enough to be replicable by the ribozyme and if these fragments self-assemble into a functional ribozyme. However, the continued self-replication of such replicases requires that the production of every essential fragment be balanced and sustained. Here, we use mathematical modeling to investigate whether and under what conditions fragmented replicases achieve continued self-replication. We first show that under a simple batch condition, the replicases fail to display continued self-replication owing to positive feedback inherent in these replicases. This positive feedback inevitably biases replication toward a subset of fragments, so that the replicases eventually fail to sustain the production of all essential fragments. We then show that this inherent instability can be resolved by small rates of random content exchange between loose compartments (i.e., horizontal transfer). In this case, the balanced production of all fragments is achieved through negative frequency-dependent selection operating in the population dynamics of compartments. This selection mechanism arises from an interaction mediated by horizontal transfer between intracellular and intercellular symmetry breaking. The horizontal transfer also ensures the presence of all essential fragments in each compartment, sustaining self-replication. Taken together, our results underline compartmentalization and horizontal transfer in the origin of the first self-replicating replicases.Comment: 14 pages, 4 figures, and supplemental materia

The Connectivities of Leaf Graphs of 2-Connected Graphs

AbstractGiven a connected graph G, denote by V the family of all the spanning trees of G. Define an adjacency relation in V as follows: the spanning trees t and t′ are said to be adjacent if for some vertex u∈V, t−u is connected and coincides with t′−u. The resultant graph G is called the leaf graph of G. The purpose of this paper is to show that if G is 2-connected with minimal degree δ, then G is (2δ−2)-connected