2,444 research outputs found
Statistical mechanics of lossy data compression using a non-monotonic perceptron
The performance of a lossy data compression scheme for uniformly biased
Boolean messages is investigated via methods of statistical mechanics. Inspired
by a formal similarity to the storage capacity problem in the research of
neural networks, we utilize a perceptron of which the transfer function is
appropriately designed in order to compress and decode the messages. Employing
the replica method, we analytically show that our scheme can achieve the
optimal performance known in the framework of lossy compression in most cases
when the code length becomes infinity. The validity of the obtained results is
numerically confirmed.Comment: 9 pages, 5 figures, Physical Review
The Network of Commuters in London
We study the directed and weighted network in which the wards of London are
vertices and two vertices are connected whenever there is at least one person
commuting to work from a ward to another. Remarkably the in-strength and
in-degree distribution tail is a power law with exponent around -2, while the
out-strength and out-degree distribution tail is exponential. We propose a
simple square lattice model to explain the observed empirical behaviour
The MSSM prediction for W+/- H-/+ production by gluon fusion
We discuss the associated W+/- H-/+ production in p p collision for the Large
Hadron Collider. A complete one-loop calculation of the loop-induced subprocess
g g -> W+/- H-/+ is presented in the framework of the Minimal Supersymmetric
Standard Model (MSSM), and the possible enhancement of the hadronic cross
section is investigated under the constraint from the squark direct-search
results and the low-energy precision data. Because of the large destructive
interplay in the quark-loop contributions between triangle-type and box-type
diagrams, the squark-loop contributions turn out to be comparable with the
quark-loop ones. In particular, the hadronic cross section via gluon fusion can
be extensively enhanced by squark-pair threshold effects in the box-type
diagrams, so that it can be as large as the hadronic cross section via the b
b-bar -> W+/- H-/+ subprocess which appears at tree level.Comment: 35 pages, 7 figures, version to appear in Physical Review
Interference between the halves of a double-well trap containing a Bose-Einstein condensate
Interference between the halves of a double-well trap containing a
Bose-Einstein condensate is studied. It is found that when the atoms in the two
wells are initially in the coherent state, the intensity exhibits collapses and
revivals, but it does not for the initial Fock states. Whether the initial
states are in the coherent states or in a Fock states, the fidelity time has
nothing to do with collision. We point out that interference and its fidelity
can be adjusted experimentally by properly preparing the number and initial
states of the system.Comment: 10 pages, 3 figures, accepted by Phy. rev.
Higgs Bundles, Gauge Theories and Quantum Groups
The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger
equation in the equivariant integration over the moduli space of Higgs bundles
is revisited. We argue that the wave functions of the corresponding
two-dimensional topological U(N) gauge theory reproduce quantum wave functions
of the Nonlinear Schr\"{o}dinger equation in the -particle sector. This
implies the full equivalence between the above gauge theory and the
-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger
equation. This also implies the explicit correspondence between the gauge
theory and the representation theory of degenerate double affine Hecke algebra.
We propose similar construction based on the gauged WZW model leading to
the representation theory of the double affine Hecke algebra. The relation with
the Nahm transform and the geometric Langlands correspondence is briefly
discussed.Comment: 48 pages, typos corrected, one reference adde
Two ways to solve ASEP
The purpose of this article is to describe the two approaches to compute
exact formulas (which are amenable to asymptotic analysis) for the probability
distribution of the current of particles past a given site in the asymmetric
simple exclusion process (ASEP) with step initial data. The first approach is
via a variant of the coordinate Bethe ansatz and was developed in work of Tracy
and Widom in 2008-2009, while the second approach is via a rigorous version of
the replica trick and was developed in work of Borodin, Sasamoto and the author
in 2012.Comment: 10 pages, Chapter in "Topics in percolative and disordered systems
Compressibility and Electronic Structure of MgB2 up to 8 GPa
The lattice parameters of MgB2 up to pressures of 8 GPa were determined using
high-resolution x-ray powder diffraction in a diamond anvil cell. The bulk
modulus, B0, was determined to be 151 +-5 GPa. Both experimental and
first-principles calculations indicate nearly isotropic mechanical behavior
under pressure. This small anisotropy is in contrast to the 2 dimensional
nature of the boron pi states. The pressure dependence of the density of states
at the Fermi level and a reasonable value for the average phonon frequency
account within the context of BCS theory for the reduction of Tc under
pressure.Comment: REVTeX file. 4 pages, 4 figure
Molecular scale contact line hydrodynamics of immiscible flows
From extensive molecular dynamics simulations on immiscible two-phase flows,
we find the relative slipping between the fluids and the solid wall everywhere
to follow the generalized Navier boundary condition, in which the amount of
slipping is proportional to the sum of tangential viscous stress and the
uncompensated Young stress. The latter arises from the deviation of the
fluid-fluid interface from its static configuration. We give a continuum
formulation of the immiscible flow hydrodynamics, comprising the generalized
Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard
interfacial free energy. Our hydrodynamic model yields interfacial and velocity
profiles matching those from the molecular dynamics simulations at the
molecular-scale vicinity of the contact line. In particular, the behavior at
high capillary numbers, leading to the breakup of the fluid-fluid interface, is
accurately predicted.Comment: 33 pages for text in preprint format, 10 pages for 10 figures with
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