12,268 research outputs found
Failure of the work-Hamiltonian connection for free energy calculations
Extensions of statistical mechanics are routinely being used to infer free
energies from the work performed over single-molecule nonequilibrium
trajectories. A key element of this approach is the ubiquitous expression
dW/dt=\partial H(x,t)/ \partial t which connects the microscopic work W
performed by a time-dependent force on the coordinate x with the corresponding
Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as
it is, cannot be used to estimate free energy changes. We discuss the
implications of this result for single-molecule experiments and atomistic
molecular simulations and point out possible avenues to overcome these
limitations
Kaluza-Klein electrically charged black branes in M-theory
We present a class of Kaluza-Klein electrically charged black p-brane
solutions of ten-dimensional, type IIA superstring theory. Uplifting to eleven
dimensions these solutions are studied in the context of M-theory. They can be
interpreted either as a p+1 extended object trapped around the eleventh
dimension along which momentum is flowing or as a boost of the following
backgrounds: the Schwarzschild black (p+1)-brane or the product of the
(10-p)-dimensional Euclidean Schwarzschild manifold with the (p+1)-dimensional
Minkowski spacetime.Comment: 16 pages, uses latex and epsf macro, figures include
Computer simulations of hard pear-shaped particles
We report results obtained from Monte Carlo simulations investi-
gating mesophase formation in two model systems of hard pear-shaped
particles. The first model considered is a hard variant of the trun-
cated Stone-Expansion model previously shown to form nematic and
smectic mesophases when embedded within a 12-6 Gay-Berne-like po-
tential [1]. When stripped of its attractive interactions, however, this system is found to lose its liquid crystalline phases. For particles of length to breadth ratio k = 3, glassy behaviour is seen at high pressures, whereas for k = 5 several bi-layer-like domains are seen, with high intradomain order but little interdomain orientational correlation. For the second model, which uses a parametric shape parameter based on the generalised Gay-Berne formalism, results are presented for particles with elongation k = 3; 4 and 5. Here, the systems with k = 3 and 4 fail to display orientationally ordered phases, but that with k = 5 shows isotropic, nematic and, unusually for a hard-particle model, interdigitated smectic A2 phases.</p
Numerical relativity in higher dimensions
We give a status report on our project targeted at performing numerical simulations of a head-on collision of non-spinning black holes in higher dimensional non-compact space-times. These simulations should help us understand black objects in higher dimensions and their stability properties. They are also relevant for the problem of black hole formation and evaporation in particle accelerators and cosmic rays. We use the symmetries of the system to reduce the problem to an effective 3+1 problem, allowing the use of existing numerical codes. As a simple application of the formalism, we present the results for the evolution of a five dimensional single black hole space-time. © 2010 IOP Publishing Ltd
Scaling properties of growing noninfinitesimal perturbations in space-time chaos
We study the spatiotemporal dynamics of random spatially distributed
noninfinitesimal perturbations in one-dimensional chaotic extended systems. We
find that an initial perturbation of finite size grows in time
obeying the tangent space dynamic equations (Lyapunov vectors) up to a
characteristic time , where is the largest Lyapunov exponent and
is a constant. For times perturbations exhibit spatial
correlations up to a typical distance . For times larger than
finite perturbations are no longer described by tangent space
equations, memory of spatial correlations is progressively destroyed and
perturbations become spatiotemporal white noise. We are able to explain these
results by mapping the problem to the Kardar-Parisi-Zhang universality class of
surface growth.Comment: 4.5 pages LaTeX (RevTeX4) format, 3 eps figs included. Submitted to
Phys Rev
Angular momentum effects in Michelson-Morley type experiments
The effect of the angular momentum density of a gravitational source on the
times of flight of light rays in an interferometer is analyzed. The calculation
is made imagining that the interferometer is at the equator of the gravity
source and, as long as possible, the metric, provided it is stationary and
axisymmetric, is not approximated. Finally, in order to evaluate the size of
the effect in the case of the Earth a weak field approximation is introduced.
For laboratory scales and non-geodesic paths the correction turns out to be
comparable with the sensitivity expected in gravitational waves interferometric
detectors, whereas it drops under the threshold of detectability when using
free (geodesic) light rays.Comment: 12 pages, LaTeX; more about the detection technique, references
added; accepted for publication in GR
Lyapunov Potential Description for Laser Dynamics
We describe the dynamical behavior of both class A and class B lasers in
terms of a Lyapunov potential. For class A lasers we use the potential to
analyze both deterministic and stochastic dynamics. In the stochastic case it
is found that the phase of the electric field drifts with time in the steady
state. For class B lasers, the potential obtained is valid in the absence of
noise. In this case, a general expression relating the period of the relaxation
oscillations to the potential is found. We have included in this expression the
terms corresponding to the gain saturation and the mean value of the
spontaneously emitted power, which were not considered previously. The validity
of this expression is also discussed and a semi-empirical relation giving the
period of the relaxation oscillations far from the stationary state is proposed
and checked against numerical simulations.Comment: 13 pages (including 7 figures) LaTeX file. To appear in Phys Rev.A
(June 1999
Axisymmetric simulations of magnetorotational core collapse: approximate inclusion of general relativistic effects
We continue our investigations of the magnetorotational collapse of stellar cores by discussing simulations performed with a modified Newtonian gravitational potential that mimics general relativistic effects. The approximate TOV gravitational potential used in our simulations captures several basic features of fully relativistic simulations quite well. In particular, it is able to correctly reproduce the behavior of models that show a qualitative change both of the dynamics and the gravitational wave signal when switching from Newtonian to fully relativistic simulations. For models where the dynamics and gravitational wave signals are already captured qualitatively correctly by a Newtonian potential, the results of the Newtonian and the approximate TOV models differ quantitatively. The collapse proceeds to higher densities with the approximate TOV potential, allowing for a more efficient amplification of the magnetic field by differential rotation. The strength of the saturation fields (∼10^15 G at the surface of the inner core) is a factor of two to three higher than in Newtonian gravity. Due to the more efficient field amplification, the influence of magnetic fields is considerably more pronounced than in the Newtonian case for some of the models. As in the Newtonian case, sufficiently strong magnetic fields slow down the core’s rotation and trigger a secular contraction phase to higher densities. More clearly than in Newtonian models, the collapsed cores of these models exhibit two different kinds of shock generation. Due to magnetic braking, a first shock wave created during the initial centrifugal bounce at subnuclear densities does not suffice for ejecting any mass, and the temporarily stabilized core continues to collapse to supranuclear densities. Another stronger shock wave is generated during the second bounce as the core exceeds nuclear matter density. The gravitational wave signal of these models does not fit into the standard classification. Therefore, in the first paper of this series we introduced a new type of gravitational wave signal, which we call type IV or “magnetic type”. This signal type is more frequent for the approximate relativistic potential than for the Newtonian one. Most of our weak-field models are marginally detectable with the current LIGO interferometer for a source located at a distance of 10 kpc. Strongly magnetized models emit a substantial fraction of their GW power at very low frequencies. A flat spectrum between 10 Hz and <∼100 kHz denotes the generation of a jet-like hydromagnetic outflow.Aloy Toras, Miguel Angel, [email protected]
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