9,607 research outputs found
Exact scaling functions for one-dimensional stationary KPZ growth
We determine the stationary two-point correlation function of the
one-dimensional KPZ equation through the scaling limit of a solvable
microscopic model, the polynuclear growth model. The equivalence to a directed
polymer problem with specific boundary conditions allows one to express the
corresponding scaling function in terms of the solution to a Riemann-Hilbert
problem related to the Painleve II equation. We solve these equations
numerically with very high precision and compare our, up to numerical rounding
exact, result with the prediction of Colaiori and Moore [1] obtained from the
mode coupling approximation.Comment: 24 pages, 6 figures, replaced with revised versio
Lowest energy states in nonrelativistic QED: atoms and ions in motion
Within the framework of nonrelativisitic quantum electrodynamics we consider
a single nucleus and electrons coupled to the radiation field. Since the
total momentum is conserved, the Hamiltonian admits a fiber
decomposition with respect to with fiber Hamiltonian . A stable atom,
resp. ion, means that the fiber Hamiltonian has an eigenvalue at the
bottom of its spectrum. We establish the existence of a ground state for
under (i) an explicit bound on , (ii) a binding condition, and (iii) an
energy inequality. The binding condition is proven to hold for a heavy nucleus
and the energy inequality for spinless electrons.Comment: 46 page
Kinetics of carbenium ion additions to methylenecycloalkanes. Cycloalkyl cation stabilities are not predominantly controlled by strain
Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
We investigate a generalised version of the recently proposed ordinal
partition time series to network transformation algorithm. Firstly we introduce
a fixed time lag for the elements of each partition that is selected using
techniques from traditional time delay embedding. The resulting partitions
define regions in the embedding phase space that are mapped to nodes in the
network space. Edges are allocated between nodes based on temporal succession
thus creating a Markov chain representation of the time series. We then apply
this new transformation algorithm to time series generated by the R\"ossler
system and find that periodic dynamics translate to ring structures whereas
chaotic time series translate to band or tube-like structures -- thereby
indicating that our algorithm generates networks whose structure is sensitive
to system dynamics. Furthermore we demonstrate that simple network measures
including the mean out degree and variance of out degrees can track changes in
the dynamical behaviour in a manner comparable to the largest Lyapunov
exponent. We also apply the same analysis to experimental time series generated
by a diode resonator circuit and show that the network size, mean shortest path
length and network diameter are highly sensitive to the interior crisis
captured in this particular data set
Laboratory process control using natural language commands from a personal computer
PC software is described which provides flexible natural language process control capability with an IBM PC or compatible machine. Hardware requirements include the PC, and suitable hardware interfaces to all controlled devices. Software required includes the Microsoft Disk Operating System (MS-DOS) operating system, a PC-based FORTRAN-77 compiler, and user-written device drivers. Instructions for use of the software are given as well as a description of an application of the system
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