– From the principle of maximum entropy for a closed system in thermal equilibrium, it is shown for the first instance, to exist a clear relation between total entropy S (in terms of arrangements of particles) and the classical expression for the force acting on a particle in a rotating frame. We determine relationships between arrangement of particles and force in the case of the gravitational...

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others...

The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline arrangements with contacts supported by a given network. In this paper, we construct the “brick polytope” of a network, o...

Amphiphilic norbornene-b-(norbornene dicarboxylic acid) diblock copolymers with different block ratios were prepared as templates for the incorporation of iron ions using an ion exchange protocol. The disordered arrangement of iron oxide particles within these copolymers was attributed to the oxidation of the iron ions and the strong interactions between iron oxide nanoparticles, particularly a...

The general approach for describing and designing complex hierarchical icosahedral structures is discussed. Structural models of icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually identical to that in diamond are derived. It is shown that icosahedral diamond-like particles can be transformed into onion-like shell structures (and vice versa) by the consecutive ...

A Monte Carlo simulation of the Ising Model, a simplified model for studying the behavior of magnetic materials at various temperatures, was constructed. This model illustrated the transition between magnetic and non-magnetic phases as temperature is increased, and showed critical-point behavior at the transition. A general system for studying the behavior of many different configurations of pa...

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been studied extensively in the context of crossing number problems. We consider a natural class of simple topological drawings of complete bipartite graphs, in ...

The Gag polyprotein is the main retroviral structural protein and is essential for the assembly and release of virus particles. In this study, we have analyzed the morphology and Gag stoichiometry of human T-cell leukemia virus type 1 (HTLV-1)-like particles and authentic, mature HTLV-1 particles by using cryogenic transmission electron microscopy (cryo-TEM) and scanning transmission electron m...