4,710 research outputs found
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion
Typical Hamiltonian liquids display exponential "Lyapunov instability", also
called "sensitive dependence on initial conditions". Although Hamilton's
equations are thoroughly time-reversible, the forward and backward Lyapunov
instabilities can differ, qualitatively. In numerical work, the expected
forward/backward pairing of Lyapunov exponents is also occasionally violated.
To illustrate, we consider many-body inelastic collisions in two space
dimensions. Two mirror-image colliding crystallites can either bounce, or not,
giving rise to a single liquid drop, or to several smaller droplets, depending
upon the initial kinetic energy and the interparticle forces. The difference
between the forward and backward evolutionary instabilities of these problems
can be correlated with dissipation and with the Second Law of Thermodynamics.
Accordingly, these asymmetric stabilities of Hamilton's equations can provide
an "Arrow of Time". We illustrate these facts for two small crystallites
colliding so as to make a warm liquid. We use a specially-symmetrized form of
Levesque and Verlet's bit-reversible Leapfrog integrator. We analyze
trajectories over millions of collisions with several equally-spaced time
reversals.Comment: 13 pages and 11 figures, prepared for Douglas Henderson's 80th
Birthday Symposium at Brigham Young University in August 2014 revised to
incorporate referee's suggestions as an acknowledgmen
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
A Study of Activated Processes in Soft Sphere Glass
On the basis of long simulations of a binary mixture of soft spheres just
below the glass transition, we make an exploratory study of the activated
processes that contribute to the dynamics. We concentrate on statistical
measures of the size of the activated processes.Comment: 17 pages, 9 postscript figures with epsf, uses harvmac.te
Rigidity of Orientationally Ordered Domains of Short Chain Molecules
By molecular dynamics simulation, discovered is a strange rigid-like nature
for a hexagonally packed domain of short chain molecules. In spite of the
non-bonded short-range interaction potential (Lennard-Jones potential) among
chain molecules, the packed domain gives rise to a resultant global moment of
inertia. Accordingly, as two domains encounter obliquely, they rotate so as to
be parallel to each other keeping their overall structures as if they were
rigid bodies.Comment: 7 pages, 5 figures, and 2 table
Scaling Solutions to 6D Gauged Chiral Supergravity
We construct explicitly time-dependent exact solutions to the field equations
of 6D gauged chiral supergravity, compactified to 4D in the presence of up to
two 3-branes situated within the extra dimensions. The solutions we find are
scaling solutions, and are plausibly attractors which represent the late-time
evolution of a broad class of initial conditions. By matching their near-brane
boundary conditions to physical brane properties we argue that these solutions
(together with the known maximally-symmetric solutions and a new class of
non-Lorentz-invariant static solutions, which we also present here) describe
the bulk geometry between a pair of 3-branes with non-trivial on-brane
equations of state.Comment: Contribution to the New Journal of Physics focus issue on Dark
Energy; 28 page
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
Kicking the Rugby Ball: Perturbations of 6D Gauged Chiral Supergravity
We analyze the axially-symmetric scalar perturbations of 6D chiral gauged
supergravity compactified on the general warped geometries in the presence of
two source branes. We find all of the conical geometries are marginally stable
for normalizable perturbations (in disagreement with some recent calculations)
and the nonconical for regular perturbations, even though none of them are
supersymmetric (apart from the trivial Salam-Sezgin solution, for which there
are no source branes). The marginal direction is the one whose presence is
required by the classical scaling property of the field equations, and all
other modes have positive squared mass. In the special case of the conical
solutions, including (but not restricted to) the unwarped `rugby-ball'
solutions, we find closed-form expressions for the mode functions in terms of
Legendre and Hypergeometric functions. In so doing we show how to match the
asymptotic near-brane form for the solution to the physics of the source
branes, and thereby how to physically interpret perturbations which can be
singular at the brane positions.Comment: 21 pages + appendices, references adde
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