Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte

Logarithmic oscillators: ideal Hamiltonian thermostats

A logarithmic oscillator (in short, log-oscillator) behaves like an ideal thermostat because of its infinite heat capacity: when it weakly couples to another system, time averages of the system observables agree with ensemble averages from a Gibbs distribution with a temperature T that is given by the strength of the logarithmic potential. The resulting equations of motion are Hamiltonian and may be implemented not only in a computer but also with real-world experiments, e.g., with cold atoms.Comment: 5 pages, 3 figures. v4: version accepted in Phys. Rev. Let

Macroscopic equations for the adiabatic piston

A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on the left and right chambers of the piston are always in equilibrium (that is the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution) after any collision with the piston. Then by using kinetic theory we derive the collision statistics from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables (namely the piston average velocity and position, the velocity variance and the temperatures of the two compartments). The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).Comment: 13 pages, 7 figures (revTeX4) The paper has been completely rewritten with new derivation and results, supplementary information can be found at http://denali.phys.uniroma1.it/~cencini/Papers/cppv07_supplements.pd

Plastic dislocation motion via nonequilibrium molecular and continuum dynamics

The classical two-dimensional close-packed triangular lattice, with nearest-neighbor spring forces, is a convenient standard material for the investigation of dislocation motion and plastic flow. Two kinds of calculations, based on this standard material, are described here: (1) Molecular Dynamics simulations, incorporating adiabatic strains described with the help of Doll's Tensor, and (2) Continuum Dynamics simulations, incorporating periodic boundaries and dislocation interaction through stress-field superposition

Comment on the calculation of forces for multibody interatomic potentials

The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition for the stress tensor gives different results depending on the radius of localization function. The differences strongly depend on the way of the force definition.Comment: 9 pages, 2 figure

Direct calculation of the hard-sphere crystal/melt interfacial free energy

We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy, $\gamma$, for a system of hard spheres of diameter $\sigma$. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with $\gamma$ = 0.62$\pm 0.01$, 0.64$\pm 0.01$ and 0.58$\pm 0.01 k_BT/\sigma^2$ for the (100), (110) and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments measuring the crystal nucleation rates from colloidal fluids of polystyrene spheres that have been interpreted [Marr and Gast, Langmuir {\bf 10}, 1348 (1994)] to give an estimate of $\gamma$ for the hard-sphere system of $0.55 \pm 0.02 k_BT/\sigma^2$, slightly lower than the directly determined value reported here.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Generativity in College Students: Comparing and Explaining the Impact of Mentoring

Preparing college students to be active contributors to the next generation is an important function of higher education. This assumption about generativity forms a cornerstone in this mixed methods study that examined generativity levels among 273 college students at a 4-year public university. MANCOVA results indicated that college students who mentor demonstrated significantly higher generativity than nonmentoring students. Interviews with 9 mentoring students revealed that, although a “seed of generativity” may have already been planted, their mentoring experience served as a “lab” for learning how to be generative. The integrated findings offer important contributions relative to leadership and social responsibility

Generativity in College Students: Comparing and Explaining the Impact of Mentoring

Preparing college students to be active contributors to the next generation is an important function of higher education. This assumption about generativity forms a cornerstone in this mixed methods study that examined generativity levels among 273 college students at a 4-year public university. MANCOVA results indicated that college students who mentor demonstrated significantly higher generativity than nonmentoring students. Interviews with 9 mentoring students revealed that, although a “seed of generativity” may have already been planted, their mentoring experience served as a “lab” for learning how to be generative. The integrated findings offer important contributions relative to leadership and social responsibility

A Dynamic Approach to the Thermodynamics of Superdiffusion

We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Levy index alpha, and using dynamical rather than probabilistic arguments.Comment: 4 pages, new revised version resubmitted to Phys. Rev. Let