23,264 research outputs found
An analytical approach to sorting in periodic potentials
There has been a recent revolution in the ability to manipulate
micrometer-sized objects on surfaces patterned by traps or obstacles of
controllable configurations and shapes. One application of this technology is
to separate particles driven across such a surface by an external force
according to some particle characteristic such as size or index of refraction.
The surface features cause the trajectories of particles driven across the
surface to deviate from the direction of the force by an amount that depends on
the particular characteristic, thus leading to sorting. While models of this
behavior have provided a good understanding of these observations, the
solutions have so far been primarily numerical. In this paper we provide
analytic predictions for the dependence of the angle between the direction of
motion and the external force on a number of model parameters for periodic as
well as random surfaces. We test these predictions against exact numerical
simulations
A model for effective interactions in binary colloidal systems of soft particles
While the density functional theory with integral equations techniques are
very efficient tools in numerical analysis of complex fluids, an analytical
insight into the phenomenon of effective interactions is still limited. In this
paper we propose a theory of binary systems which results in a relatively
simple analytical expression combining arbitrary microscopic potentials into
the effective interaction. The derivation is based on translating many particle
Hamiltonian including particle-depletant and depletant-depletant interactions
into the occupation field language. Such transformation turns the partition
function into multiple Gaussian integrals, regardless of what microscopic
potentials are chosen. In result, we calculate the effective Hamiltonian and
discuss when our formula is a dominant contribution to the effective
interactions. Our theory allows us to analytically reproduce several important
characteristics of systems under scrutiny. In particular, we analyze the
effective attraction as a demixing factor in the binary systems of Gaussian
particles, effective interactions in the binary mixtures of Yukawa particles
and the system of particles consisting of both repulsive core and
attractive/repulsive Yukawa interaction tail, for which we reproduce the
'attraction-through-repulsion' and 'repulsion-through-attraction' effects.Comment: Second version of article, after major revision due to the comments
from reviewers. Includes overhauled introductory section, new, more compact
derivation and more elaborate examples than previousl
The Effect of a Refractory Period on the Power Spectrum of Neuronal Discharge
The interspike intervals in steady-state neuron firing are assumed to be independently and identically distributed random variables. In the simplest model discussed, each interval is assumed to be the sum of a random neuron refractory period and a statistically independent interval due to a stationary external process, whose statistics are assumed known. The power spectral density (hence the autocorrelation) of the composite neuron-firing renewal process is derived from the known spectrum of the external process and from the unknown spectrum of the neuron-refraction process. The results are applied to spike trains recorded in a previous study [2] of single neurons in the visual cortex of an awake monkey. Two models are demonstrated that may produce peaks in the power spectrum near 40 Hz
Short-range potentials from QCD at order
We systematically compute the effective short-range potentials arising from
second order QCD-diagrams related to bound states of quarks, antiquarks, and
gluons. Our formalism relies on the assumption that the exchanged gluons are
massless, while the constituent gluons as well as the lightest quarks acquire a
nonvanishing constituent mass because of confinement. The potentials we obtain
include the first relativistic corrections, thus spin-spin terms, spin-orbit
terms, etc. Such effective potentials are expected to be relevant for the
building of accurate potential models describing usual hadrons as well as
exotic ones like glueballs and hybrids. In particular, we compute
for the first time an effective quark-gluon potential, and show the existence
of a quadrupolar interaction term in this case. We also discuss the influence
of a possible nonzero mass for the exchanged gluons.Comment: 33 pages, 4 tables and 12 figures ; typos correcte
Classcial Bifurcation and Enhancement of Quantum Shells --- Systematic Analysis of Reflection-Asymmetric Deformed Oscillator ---
Correspondence between classical periodic orbits and quantum shell structure
is investigated for a reflection-asymmetric deformed oscillator model as a
function of quadrupole and octupole deformation parameters. Periodic orbit
theory reveals several aspects of quantum level structure for this
non-integrable system. Good classical- quantum correspondence is obtained in
the Fourier transform of the quantum level density, and importance of periodic
orbit bifurcation is demonstrated. Systematic survey of the local minima of
shell energies in the two-dimensional deformation parameter space shows that
prominent shell structures do emerge at finite values of the octupole
parameter. Correspondences between the regions exhibiting strong shell effects
and the classical bifurcation lines are investigated, and significance of these
bifurcations is indicated.Comment: 17 pages, REVTeX. 23 PostScript figures (not appended due to
excessive size, 3,860kb in total) are avalilable from K.A.
([email protected]) upon reques
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