The free rigid body dynamics: generalized versus classic

In this paper we analyze the normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ real symmetric matrix. A consequence of the main results is that any first-order autonomous three-dimensional differential equation possessing two independent quadratic constants of motion which admits a positive/negative definite linear combination, is affinely equivalent to the classical "relaxed" free rigid body dynamics with linear controls.Comment: 12 page

The cultural shaping of compassion

In this chapter, we first review the existing literature on cross-cultural studies on compassion. While cultural similarities exist, we demonstrate cultural differences in the conception, experience, and expression of compassion. Then we present our own work on the cultural shaping of compassion by introducing Affect Valuation Theory ( e.g., Tsai, Knutson, & Fung, 2006), our theoretical framework. We show how the desire to avoid feeling negative partly explains cultural differences in conceptualizations and expressions of compassion. Specifically, the more people want to avoid feeling negative, the more they focus on the positive (e.g., comforting memories) than the negative (e.g., the pain of someone\u27s death) when responding to others\u27 suffering, and the more they regard responses as helpful that focus on the positive (vs. negative). Finally, we discuss implications of our work for counseling, health care, and public service settings, as well as for interventions that aim to promote compassion

Simplicial Quantum Gravity on a Randomly Triangulated Sphere

We study 2D quantum gravity on spherical topologies employing the Regge calculus approach with the dl/l measure. Instead of the normally used fixed non-regular triangulation we study random triangulations which are generated by the standard Voronoi-Delaunay procedure. For each system size we average the results over four different realizations of the random lattices. We compare both types of triangulations quantitatively and investigate how the difference in the expectation value of the squared curvature, $R^2$, for fixed and random triangulations depends on the lattice size and the surface area A. We try to measure the string susceptibility exponents through finite-size scaling analyses of the expectation value of an added $R^2$-interaction term, using two conceptually quite different procedures. The approach, where an ultraviolet cut-off is held fixed in the scaling limit, is found to be plagued with inconsistencies, as has already previously been pointed out by us. In a conceptually different approach, where the area A is held fixed, these problems are not present. We find the string susceptibility exponent $\gamma_{str}'$ in rough agreement with theoretical predictions for the sphere, whereas the estimate for $\gamma_{str}$ appears to be too negative. However, our results are hampered by the presence of severe finite-size corrections to scaling, which lead to systematic uncertainties well above our statistical errors. We feel that the present methods of estimating the string susceptibilities by finite-size scaling studies are not accurate enough to serve as testing grounds to decide about a success or failure of quantum Regge calculus.Comment: LaTex, 29 pages, including 9 figure

How (In)accurate Are Demand Forecasts in Public Works Projects? The Case of Transportation

This article presents results from the first statistically significant study of traffic forecasts in transportation infrastructure projects. The sample used is the largest of its kind, covering 210 projects in 14 nations worth US$59 billion. The study shows with very high statistical significance that forecasters generally do a poor job of estimating the demand for transportation infrastructure projects. The result is substantial downside financial and economic risks. Such risks are typically ignored or downplayed by planners and decision makers, to the detriment of social and economic welfare. For nine out of ten rail projects passenger forecasts are overestimated; average overestimation is 106 percent. This results in large benefit shortfalls for rail projects. For half of all road projects the difference between actual and forecasted traffic is more than plus/minus 20 percent. Forecasts have not become more accurate over the 30-year period studied. If techniques and skills for arriving at accurate demand forecasts have improved over time, as often claimed by forecasters, this does not show in the data. The causes of inaccuracy in forecasts are different for rail and road projects, with political causes playing a larger role for rail than for road. The cure is transparency, accountability, and new forecasting methods. The challenge is to change the governance structures for forecasting and project development. The article shows how planners may help achieve this.Comment: arXiv admin note: text overlap with arXiv:1302.2544, arXiv:1303.6571, arXiv:1302.364

End-effects of strongly charged polyelectrolytes - a molecular dynamics study

We investigate end-effects in the ion distribution around strongly charged, flexible polyelectrolytes with a quenched charge distribution by molecular dynamics simulations of dilute polyelectrolyte solutions. We take the counterions explicitly into account and calculate the full Coulomb interaction via an Ewald summation method. We find that the free counterions of the solution are distributed in such a way that a fraction of the chain charges is effectively neutralized. This in turn leads to an effective charge distribution which is similar to those found for weakly charged titrating polyelectrolytes that have an annealed charge distribution. The delicate interplay between the electrostatic interactions, the chain conformation and the counterion distribution is studied in detail as a function of different system parameters such as the chain length Nm, the charge fraction f, the charged particle density rho, the ionic strength and the solvent quality. Comparisons are made with predictions from a scaling theory.Comment: 20 pages, 10 figures. J. Chem. Phys, to appear June 200

Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence

Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation