Jan Tobochnik

Prediction of emerging technologies based on analysis of the US patent citation network

The network of patents connected by citations is an evolving graph, which provides a representation of the innovation process. A patent citing another implies that the cited patent reflects a piece of previously existing knowledge that the citing patent builds upon. A methodology presented here (1) identifies actual clusters of patents: i.e., technological branches, and (2) gives predictions about the temporal changes of the structure of the clusters. A predictor, called the citation vector, is defined for characterizing technological development to show how a patent cited by other patents belongs to various industrial fields. The clustering technique adopted is able to detect the new emerging recombinations, and predicts emerging new technology clusters. The predictive ability of our new method is illustrated on the example of USPTO subcategory 11, Agriculture, Food, Textiles. A cluster of patents is determined based on citation data up to 1991, which shows significant overlap of the class 442 formed at the beginning of 1997. These new tools of predictive analytics could support policy decision making processes in science and technology, and help formulate recommendations for action.

Monte Carlo simulation of hard spheres near random closest packing using spherical boundary conditions

Monte Carlo simulations were performed for hard disks on the surface of an ordinary sphere and hard spheres on the surface of a four‐dimensional hypersphere. Starting from the low density fluid the density was increased to obtain metastable amorphous states at densities higher than previously achieved. Above the freezing density the inverse pressure decreases linearly with density, reaching zero at packing fractions equal to 68% for hard spheres and 84% for hard disks. Using these new estimates for random closest packing and coefficients from the virial series we obtain an equation of state which fits all the data up to random closest packing. Usually, the radial distribution function showed the typical split second peak characteristic of amorphous solids and glasses. High density systems which lacked this split second peak and showed other sharp peaks were interpreted as signaling the onset of crystal nucleation.

Understanding temperature and chemical potential using computer simulations

Several Monte Carlo algorithms and applications that are useful for understanding the concepts of temperature and chemical potential are discussed. We then introduce a generalization of the demon algorithm that measures the chemical potential and is suitable for simulating systems with variable particle number.

Granular collapse as a percolation transition.

Inelastic collapse is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a transition between a state containing small collapsed clusters and a state dominated by a large collapsed cluster. The transition is analogous to that of a percolation transition. At the transition the number of clusters n(s) of size s scales as n(s) approximately s(-tau) with tau approximately equal to 2.7.

Universal conductivity in the two-dimensional boson Hubbard model

We use quantum Monte Carlo methods to evaluate the conductivity [sigma] of the two-dimensional disordered boson Hubbard model at the superfluid--Bose-glass phase boundary. At the critical point for particle density [rho]=0.5, we find [sigma][sub [ital c]]=(0.45[plus minus]0.07)[sigma][sub [ital Q]], where [sigma][sub [ital Q]]=[ital e][sub *][sup 2]/[ital h] from a finite-size scaling analysis of the superfluid density. We obtain [sigma][sub [ital c]]=(0.47[plus minus]0.08)[sigma][sub [ital Q]] from a direct calculation of the current-current correlation function. Simulations at the critical points for other particle densities, [rho]=0.75 and 1.0, give similar values for [sigma]. We discuss possible origins of the difference in this value from that recently obtained by other numerical approaches.

Kinetics of a First-Order Phase Transition: Computer Simulations and Theory

We make a quantitative comparison between the predictions of the Becker-Döring equations and computer simulations on a model of a quenched binary A-B alloy. The atoms are confined to the vertices of a simple cubic lattice, interact through attractive nearest neighbor interactions, and move by interchanges of nearest neighbor pairs (Kawasaki dynamics). We study in particular the time evolution of the number of clusters of A atoms of each size, at four different concentrations: ρA=0.035, 0.05, 0.075, and 0.1 atoms per lattice site. The temperature is 0.59 times the critical temperature. At this temperature the equilibrium concentration of A atoms in the B-rich phase is ρAeq=0.0145 atoms/lattice site. The coefficients entering the Becker-Döring equations are obtained by extrapolation from previously published low-density calculations, leaving the time scale as the only adjustable parameter. We find good agreement at the three lower densities. At 10% density the agreement is, as might be expected, less satisfactory but still fairly good-indicating a quite wide range of utility for the Becker-Döring equations.

Teaching statistical physics by thinking about models and algorithms

We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students’ incomplete mental images by models that are physically accurate. In some cases it is sufficient to discuss the results of an algorithm or the behavior of a model rather than having students write a program.

Resource letter CPPPT-1: Critical point phenomena and phase transitions

This Resource Letter provides a guide to the literature on critical point phenomena and phase transitions. Journal articles and books are cited for the following topics: continuous phase transitions, critical points, model systems with special attention to the Ising model and the Kosterlitz–Thouless transition, mean-field theory, computer simulation methods, scaling, universality, and the renormalization group.

Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different from the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.

Efficient random walk algorithm for computing conductivity in continuum percolation systems

Random walks can be used to obtain the diffusion constant and thus the conductivity for continuum percolation problems. This paper presents an efficient algorithm that allows walkers to move very large distances in one step. The algorithm uses a first‐passage time distribution for d‐dimensional spherical surfaces. Results are given for overlapping nonconducting disks in two dimensions. Depending on the density of disks, it is found that the present algorithm is about 5 to 50 times faster than an equivalent algorithm using fixed step lengths.