A simple Monte Carlo model for crowd dynamics

In this paper we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of non-equilibrium hard-disk fluids and discuss general implications of our model.Comment: to be published in Physical Review

On the relationship of the scaled phase space and Skyrme-coherent state treatments of proton antiproton annihilation at rest

We discuss pion multiplicities and single pion momentum spectra from proton antiproton annihilation at rest. Both the scaled phase space model and the Skyrme-coherent state approach describe these observables well. In the coherent state approach the puzzling size of the scale parameter relating the phase space integrals for different multiplicities is replaced by a well defined weight function. The strength of this function is determined by the intensity of the classical pion field and its spatial extent is of order 1 fm.Comment: 11 pages including 4 figures(postscript

Coherent Pion Radiation From Nucleon Antinucleon Annihilation

A unified picture of nucleon antinucleon annihilation into pions emerges from a classical description of the pion wave produced in annihilation and the subsequent quantization of that wave as a coherent state. When the constraints of energy-momentum and iso-spin conservation are imposed on the coherent state, the pion number distribution and charge ratios are found to be in excellent agreement with experiment.Comment: LaTex, 8 text pages, 1 PostScript figure, PSI-PR-93-2

A Relationship Built to Impact Instruction: Developing and Sustaining Productive Partnerships Between Mathematics Specialists and Principals

How does the mathematics specialist provide a profound and lasting impact on instruction? We believe that a productive partnership between the principal and specialist, which we will call the principal-specialist relationship, is at the crux of the matter. When the principal-specialist relationship is built upon a foundation of a shared vision, clear roles, communication, and trust, both the teachers and students in the school benefit. We will explore the impact of the principal-specialist relationship on teacher success during the era of distance learning as necessitated by the COVID-19 pandemic. In order to explore how these ideas come alive in the field, we gathered survey responses and conducted personal interviews with mathematics specialists in a variety of roles. This article examines ways in which the principal-specialist relationship supports successful mathematics instruction beginning with a review of contemporary literature. In the form of short vignettes throughout the paper, we illustrate the roles of the mathematics specialist and how those roles were adapted for online learning environments. Our findings revealed that a unifying vision for mathematics instruction is essential for attaining maximum impact on student achievement

Coherent state formulation of pion radiation from nucleon antinucleon annihilation

We assume that nucleon antinucleon annihilation is a fast process leading to a classical coherent pion pulse. We develop the quantum description of such pion waves based on the method of coherent states. We study the consequences of such a description for averages of charge types and moments of distributions of pion momenta with iso-spin and four-momentum conservation taken into account. We briefly discuss the applicability of our method to annihilation at rest, where we find agreement with experiment, and suggest other avenues for its use.Comment: 24 pages, 3 figures, 1 table, PSI-preprin

Multivariate Anisotropic Interpolation on the Torus

We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of interpolation. These conditions and the investigation of the error especially take different levels of smoothness along certain directions into account

An Inward-Facing Conformation of a Putative Metal-Chelate–Type ABC Transporter

The crystal structure of a putative metal-chelate–type adenosine triphosphate (ATP)–binding cassette (ABC) transporter encoded by genes HI1470 and HI1471 of Haemophilus influenzae has been solved at 2.4 angstrom resolution. The permeation pathway exhibits an inward-facing conformation, in contrast to the outward-facing state previously observed for the homologous vitamin B12 importer BtuCD. Although the structures of both HI1470/1 and BtuCD have been solved in nucleotide-free states, the pairs of ABC subunits in these two structures differ by a translational shift in the plane of the membrane that coincides with a repositioning of the membrane-spanning subunits. The differences observed between these ABC transporters involve relatively modest rearrangements and may serve as structural models for inward- and outward-facing conformations relevant to the alternating access mechanism of substrate translocation

Two-dimensional frustrated Heisenberg model: Variational study

The stability of the ferromagnetic phase of the 2D quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnon are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function of new type. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain the accurate estimate of the transition point and to study the character of the phase transition.Comment: 10 pages, 4 figures, RevTe

Studying Kaon-pion S-wave scattering in K-matrix formalism

We generalize our previous work on \pi\pi scattering to K\pi scattering, and re-analyze the experiment data of K\pi scattering below 1.6 GeV. Without any free parameter, we explain K\pi I=3/2 S-wave phase shift very well by using t-channel rho and u-channel K^* meson exchange. With the t-channel and u-channel meson exchange fixed as the background term, we fit the K\pi I=1/2 S-wave data of the LASS experiment quite well by introducing one or two s-channel resonances. It is found that there is only one s-channel resonance between K\pi threshold and 1.6 GeV, i.e., K_0^*(1430) with a mass around 1438~1486 MeV and a width about 346 MeV, while the t-channel rho exchange gives a pole at (450-480i) MeV for the amplitude.Comment: REVTeX4 file, 11 pages and 3 figure