1,489 research outputs found
Embedding Brans-Dicke gravity into electroweak theory
We argue that a version of the four dimensional Brans-Dicke theory can be
embedded in the standard flat spacetime electroweak theory. The embedding
involves a change of variables that separates the isospin from the hypercharge
in the electroweak theory.Comment: 4 pages, no figures; replaced to match published versio
Evidence of Cooper pair pumping with combined flux and voltage control
We have experimentally demonstrated pumping of Cooper pairs in a
single-island mesoscopic structure. The island was connected to leads through
SQUID (Superconducting Quantum Interference Device) loops. Synchronized flux
and voltage signals were applied whereby the Josephson energies of the SQUIDs
and the gate charge were tuned adiabatically. From the current-voltage
characteristics one can see that the pumped current increases in 1e steps which
is due to quasiparticle poisoning on the measurement time scale, but we argue
that the transport of charge is due to Cooper pairs.Comment: 4 page
Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem
We present a numerical Monte Carlo analysis of a continuos spin Ising chain
that can describe the statistical proterties of folded proteins. We find that
depending on the value of the Metropolis temperature, the model displays the
three known nontrivial phases of polymers: At low temperatures the model is in
a collapsed phase, at medium temperatures it is in a random walk phase, and at
high temperatures it enters the self-avoiding random walk phase. By
investigating the temperature dependence of the specific energy we confirm that
the transition between the collapsed phase and the random walk phase is a phase
transition, while the random walk phase and self-avoiding random walk phase are
separated from each other by a cross-over transition. We also compare the
predictions of the model to a phenomenological elastic energy formula, proposed
by Huang and Lei to describe folded proteins.Comment: 12 pages, 23 figures, RevTeX 4.
Magnetic Geometry and the Confinement of Electrically Conducting Plasmas
We develop an effective field theory approach to inspect the electromagnetic
interactions in an electrically neutral plasma, with an equal number of
negative and positive charge carriers. We argue that the static equilibrium
configurations within the plasma are topologically stable solitons, that
describe knotted and linked fluxtubes of helical magnetic fields.Comment: 9 pages 1 ps-figur
Partially Dual variables in SU(2) Yang-Mills Theory
We propose a reformulation of SU(2) Yang-Mills theory in terms of new
variables. These variables are appropriate for describing the theory in its
infrared limit, and indicate that it admits knotlike configurations as stable
solitons. As a consequence we arrive at a dual picture of the Yang-Mills theory
where the short distance limit describes asymptotically free, massless point
gluons and the large distance limit describes extended, massive knotlike
solitons.Comment: 4 pages, revtex twocolum
Mean-Field Dynamics: Singular Potentials and Rate of Convergence
We consider the time evolution of a system of identical bosons whose
interaction potential is rescaled by . We choose the initial wave
function to describe a condensate in which all particles are in the same
one-particle state. It is well known that in the mean-field limit the quantum -body dynamics is governed by the nonlinear Hartree
equation. Using a nonperturbative method, we extend previous results on the
mean-field limit in two directions. First, we allow a large class of singular
interaction potentials as well as strong, possibly time-dependent external
potentials. Second, we derive bounds on the rate of convergence of the quantum
-body dynamics to the Hartree dynamics.Comment: Typos correcte
Delocalization and Diffusion Profile for Random Band Matrices
We consider Hermitian and symmetric random band matrices in dimensions. The matrix entries , indexed by x,y \in
(\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy}
= \E |h_{xy}|^2. We assume that is negligible if exceeds the
band width . In one dimension we prove that the eigenvectors of are
delocalized if . We also show that the magnitude of the matrix
entries \abs{G_{xy}}^2 of the resolvent is self-averaging
and we compute \E \abs{G_{xy}}^2. We show that, as and , the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator
whose diffusion constant we compute. Similar results are obtained in higher
dimensions
Solitons and Collapse in the lambda-repressor protein
The enterobacteria lambda phage is a paradigm temperate bacteriophage. Its
lysogenic and lytic life cycles echo competition between the DNA binding
-repressor (CI) and CRO proteins. Here we scrutinize the structure,
stability and folding pathways of the -repressor protein, that
controls the transition from the lysogenic to the lytic state. We first
investigate the super-secondary helix-loop-helix composition of its backbone.
We use a discrete Frenet framing to resolve the backbone spectrum in terms of
bond and torsion angles. Instead of four, there appears to be seven individual
loops. We model the putative loops using an explicit soliton Ansatz. It is
based on the standard soliton profile of the continuum nonlinear Schr\"odinger
equation. The accuracy of the Ansatz far exceeds the B-factor fluctuation
distance accuracy of the experimentally determined protein configuration. We
then investigate the folding pathways and dynamics of the -repressor
protein. We introduce a coarse-grained energy function to model the backbone in
terms of the C atoms and the side-chains in terms of the relative
orientation of the C atoms. We describe the folding dynamics in terms
of relaxation dynamics, and find that the folded configuration can be reached
from a very generic initial configuration. We conclude that folding is
dominated by the temporal ordering of soliton formation. In particular, the
third soliton should appear before the first and second. Otherwise, the DNA
binding turn does not acquire its correct structure. We confirm the stability
of the folded configuration by repeated heating and cooling simulations
Counter Machines and Distributed Automata: A Story about Exchanging Space and Time
We prove the equivalence of two classes of counter machines and one class of
distributed automata. Our counter machines operate on finite words, which they
read from left to right while incrementing or decrementing a fixed number of
counters. The two classes differ in the extra features they offer: one allows
to copy counter values, whereas the other allows to compute copyless sums of
counters. Our distributed automata, on the other hand, operate on directed path
graphs that represent words. All nodes of a path synchronously execute the same
finite-state machine, whose state diagram must be acyclic except for
self-loops, and each node receives as input the state of its direct
predecessor. These devices form a subclass of linear-time one-way cellular
automata.Comment: 15 pages (+ 13 pages of appendices), 5 figures; To appear in the
proceedings of AUTOMATA 2018
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
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