1,769 research outputs found
Discontinuous percolation transitions in real physical systems
We study discontinuous percolation transitions (PT) in the diffusion-limited
cluster aggregation model of the sol-gel transition as an example of real
physical systems, in which the number of aggregation events is regarded as the
number of bonds occupied in the system. When particles are Brownian, in which
cluster velocity depends on cluster size as with
, a larger cluster has less probability to collide with other
clusters because of its smaller mobility. Thus, the cluster is effectively more
suppressed in growth of its size. Then the giant cluster size increases
drastically by merging those suppressed clusters near the percolation
threshold, exhibiting a discontinuous PT. We also study the tricritical
behavior by controlling the parameter , and the tricritical point is
determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure
Radial Spin Helix in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling
We suggest a long-lived spin polarization structure, a radial spin helix, and
study its relaxation dynamics. For this purpose, starting with a simple and
physically clear consideration of spin transport, we derive a system of
equations for spin polarization density and find its general solution in the
axially symmetric case. It is demonstrated that the radial spin helix of a
certain period relaxes slower than homogeneous spin polarization and plain spin
helix. Importantly, the spin polarization at the center of the radial spin
helix stays almost unchanged at short times. At longer times, when the initial
non-exponential relaxation region ends, the relaxation of the radial spin helix
occurs with the same time constant as that describing the relaxation of the
plain spin helix.Comment: 9 pages, 7 figure
The role of the nature of the noise in the thermal conductance of mechanical systems
Focussing on a paradigmatic small system consisting of two coupled damped
oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the
thermal conductance. For white noises, we prove that the L\'evy-It\^o
composition (Lebesgue measure) of the noise is irrelevant for the thermal
conductance of a non-equilibrium linearly coupled chain, which signals the
independence between mechanical and thermodynamical properties. On the other
hand, for the non-linearly coupled case, the two types of properties mix and
the explicit definition of the noise plays a central role.Comment: 9 pages, 2 figures. To be published in Physical Review
Analog approach for the eigen-decomposition of positive definite matrices
AbstractThis paper proposes an analog approach for performing the eigen-decomposition of positive definite matrices. We show analytically and by simulations that the proposed circuit is guaranteed to converge to the desired eigenvectors and eigenvalues of positive definite matrices
Energy distribution and cooling of a single atom in an optical tweezer
We investigate experimentally the energy distribution of a single rubidium
atom trapped in a strongly focused dipole trap under various cooling regimes.
Using two different methods to measure the mean energy of the atom, we show
that the energy distribution of the radiatively cooled atom is close to
thermal. We then demonstrate how to reduce the energy of the single atom, first
by adiabatic cooling, and then by truncating the Boltzmann distribution of the
single atom. This provides a non-deterministic way to prepare atoms at low
microKelvin temperatures, close to the ground state of the trapping potential.Comment: 9 pages, 6 figures, published in PR
Charged particle display
An optical shutter based on charged particles is presented. The output light
intensity of the proposed device has an intrinsic dependence on the
interparticle spacing between charged particles, which can be controlled by
varying voltages applied to the control electrodes. The interparticle spacing
between charged particles can be varied continuously and this opens up the
possibility of particle based displays with continuous grayscale.Comment: typographic errors corrected in Eqs (37) and (39); published in
Journal of Applied Physics; doi:10.1063/1.317648
The ideal gas as an urn model: derivation of the entropy formula
The approach of an ideal gas to equilibrium is simulated through a
generalization of the Ehrenfest ball-and-box model. In the present model, the
interior of each box is discretized, {\it i.e.}, balls/particles live in cells
whose occupation can be either multiple or single. Moreover, particles
occasionally undergo random, but elastic, collisions between each other and
against the container walls. I show, both analitically and numerically, that
the number and energy of particles in a given box eventually evolve to an
equilibrium distribution which, depending on cell occupations, is binomial
or hypergeometric in the particle number and beta-like in the energy.
Furthermore, the long-run probability density of particle velocities is
Maxwellian, whereas the Boltzmann entropy exactly reproduces the
ideal-gas entropy. Besides its own interest, this exercise is also relevant for
pedagogical purposes since it provides, although in a simple case, an explicit
probabilistic foundation for the ergodic hypothesis and for the maximum-entropy
principle of thermodynamics. For this reason, its discussion can profitably be
included in a graduate course on statistical mechanics.Comment: 17 pages, 3 figure
Dynamic roughening and fluctuations of dipolar chains
Nonmagnetic particles in a carrier ferrofluid acquire an effective dipolar
moment when placed in an external magnetic field. This fact leads them to form
chains that will roughen due to Brownian motion when the magnetic field is
decreased. We study this process through experiments, theory and simulations,
three methods that agree on the scaling behavior over 5 orders of magnitude.
The RMS width goes initially as , then as before it
saturates. We show how these results complement existing results on polymer
chains, and how the chain dynamics may be described by a recent non-Markovian
formulation of anomalous diffusion.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Fcc-bcc transition for Yukawa interactions determined by applied strain deformation
Calculations of the work required to transform between bcc and fcc phases
yield a high-precision bcc-fcc transition line for monodisperse point Yukawa
(screened-Couloumb) systems. Our results agree qualitatively but not
quantitatively with previously published simulations and phenomenological
criteria for the bcc-fcc transition. In particular, the bcc-fcc-fluid triple
point lies at a higher inverse screening length than previously reported.Comment: RevTex4, 9 pages, 6 figures. Discussion of phase coexistence
extended, a few other minor clarifications added, referencing improved.
Accepted for publication by Physical Review
A mechanical Turing machine: blueprint for a biomolecular computer
We describe a working mechanical device that embodies the theoretical computing machine of Alan Turing, and as such is a universal programmable computer. The device operates on three-dimensional building blocks by applying mechanical analogues of polymer elongation, cleavage and ligation, movement along a polymer, and control by molecular recognition unleashing allosteric conformational changes. Logically, the device is not more complicated than biomolecular machines of the living cell, and all its operations are part of the standard repertoire of these machines; hence, a biomolecular embodiment of the device is not infeasible. If implemented, such a biomolecular device may operate in vivo, interacting with its biochemical environment in a program-controlled manner. In particular, it may ‘compute’ synthetic biopolymers and release them into its environment in response to input from the environment, a capability that may have broad pharmaceutical and biological applications
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