2D and 3D Dense-Fluid Shear Flows via Nonequilibrium Molecular Dynamics. Comparison of Time-and-Space-Averaged Tensor Temperature and Normal Stresses from Doll's, Sllod, and Boundary-Driven Shear Algorithms

Homogeneous shear flows (with constant strainrate du/dy) are generated with the Doll's and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. The nonlinear stress differences are small, but significant, in both two and three space dimensions. In homogeneous systems the sign and magnitude of the shearplane stress difference, P(xx) - P(yy), depend on both the thermostat type and the chosen shearflow algorithm. The Doll's and Sllod algorithms predict opposite signs for this stress difference, with the Sllod approach definitely wrong, but somewhat closer to the (boundary-driven) truth. Neither of the homogeneous shear algorithms predicts the correct ordering of the kinetic temperatures, T(xx) > T(zz) > T(yy).Comment: 34 pages with 12 figures, under consideration by Physical Review

Microscopic and Macroscopic Stress with Gravitational and Rotational Forces

Many recent papers have questioned Irving and Kirkwood's atomistic expression for stress. In Irving and Kirkwood's approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate [1] a fluid in a gravitational field and [2] a steadily rotating solid. For both problems we choose conditions where the two stress contributions, potential and kinetic, are significant. The analytic force-balance solutions of both these problems agree very well with a smooth-particle interpretation of the atomistic Irving-Kirkwood stress tensor.Comment: Fifteen pages with seven figures, revised according to referees' suggestions at Physical Review E. See also Liu and Qiu's arXiv contribution 0810.080

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

An automatic lightning detection and photographic system

Conventional 35-mm camera is activated by an electronic signal every time lightning strikes in general vicinity. Electronic circuit detects lightning by means of antenna which picks up atmospheric radio disturbances. Camera is equipped with fish-eye lense, automatic shutter advance, and small 24-hour clock to indicate time when exposures are made

Exact Wave Solutions to 6D Gauged Chiral Supergravity

We describe a broad class of time-dependent exact wave solutions to 6D gauged chiral supergravity with two compact dimensions. These 6D solutions are nontrivial warped generalizations of 4D pp-waves and Kundt class solutions and describe how a broad class of previously-static compactifications from 6D to 4D (sourced by two 3-branes) respond to waves moving along one of the uncompactified directions. Because our methods are generally applicable to any higher dimensional supergravity they are likely to be of use for finding the supergravity limit of time-dependent solutions in string theory. The 6D solutions are interesting in their own right, describing 6D shock waves induced by high energy particles on the branes, and as descriptions of the near-brane limit of the transient wavefront arising from a local bubble-nucleation event on one of the branes, such as might occur if a tension-changing phase transition were to occur.Comment: 22 pages, 1 figure. Minor clarifications added. Accepted in JHE

Nonlinear Stresses and Temperatures in Transient Adiabatic and Shear Flows via Nonequilibrium Molecular Dynamics -- Three Definitions of Temperature

We compare nonlinear stresses and temperatures for adiabatic shear flows, using up to 262,144 particles, with those from corresponding homogeneous and inhomogeneous flows. Two varieties of kinetic temperature tensors are compared to the configurational temperatures. This comparison leads to an improved form for the local and instantaneous smooth-particle averaged stream velocity and to a recognition of rotational contributions to the configurational temperature.Comment: 16 pages, 8 figures, stimulated by Denis Evans' comments on Hoover et alii, Physical Review E 78, 046701 (2008). Augmented 30 January 2009 in response to referees' comments at Physical Review

Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering

In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear properties of this new dynamical system by numerically calculating its Lyapunov exponents. Based on a revised method for computing Lyapunov exponents, which employs periodic orthonormalization with a constraint, we present results for the Lyapunov exponents and related quantities in equilibrium and nonequilibrium. Finally, we check whether we obtain the same relations between quantities characterizing the microscopic chaotic dynamics and quantities characterizing macroscopic transport as obtained for conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript

Configurational temperature control for atomic and molecular systems

A new configurational temperature thermostat suitable for molecules with holonomic constraints is derived. This thermostat has a simple set of motion equations, can generate the canonical ensemble in both position and momentum space, acts homogeneously through the spatial coordinates, and does not intrinsically violate the constraints. Our new configurational thermostat is closely related to the kinetic temperature Nosé-Hoover thermostat with feedback coupled to the position variables via a term proportional to the net molecular force. We validate the thermostat by comparing equilibrium static and dynamic quantities for a fluid of n-decane molecules under configurational and kinetic temperature control. Practical aspects concerning the implementation of the new thermostat in a molecular dynamics code and the potential applications are discussed