5,369 research outputs found
Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries
We consider a driven diffusive system with two types of particles, A and B,
coupled at the ends to reservoirs with fixed particle densities. To define
stochastic dynamics that correspond to boundary reservoirs we introduce
projection measures. The stationary state is shown to be approached dynamically
through an infinite reflection of shocks from the boundaries. We argue that
spontaneous symmetry breaking observed in similar systems is due to placing
effective impurities at the boundaries and therefore does not occur in our
system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure
Estimating process capability index Cpm using a bootstrap sequential sampling procedure
Construction of a confidence interval for process capability index CPM is often based on a normal approximation with fixed sample size. In this article, we describe a different approach in constructing a fixed-width confidence interval for process capability index CPM with a preassigned accuracy by using a combination of bootstrap and sequential sampling schemes. The optimal sample size required to achieve a preassigned confidence level is obtained using both two-stage and modified two-stage sequential procedures. The procedure developed is also validated using an extensive simulation study.<br /
Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
We study a one-dimensional anisotropic exclusion process describing particles
injected at the origin, moving to the right on a chain of sites and being
removed at the (right) boundary. We construct the steady state and compute the
density profile, exact expressions for all equal-time n-point density
correlation functions and the time-dependent two-point function in the steady
state as functions of the injection and absorption rates. We determine the
phase diagram of the model and compare our results with predictions from
dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P
Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system
We study spontaneous symmetry breaking in a one-dimensional driven
two-species stochastic cellular automaton with parallel sublattice update and
open boundaries. The dynamics are symmetric with respect to interchange of
particles. Starting from an empty initial lattice, the system enters a symmetry
broken state after some time T_1 through an amplification loop of initial
fluctuations. It remains in the symmetry broken state for a time T_2 through a
traffic jam effect. Applying a simple martingale argument, we obtain rigorous
asymptotic estimates for the expected times ~ L ln(L) and ln() ~ L,
where L is the system size. The actual value of T_1 depends strongly on the
initial fluctuation in the amplification loop. Numerical simulations suggest
that T_2 is exponentially distributed with a mean that grows exponentially in
system size. For the phase transition line we argue and confirm by simulations
that the flipping time between sign changes of the difference of particle
numbers approaches an algebraic distribution as the system size tends to
infinity.Comment: 23 pages, 7 figure
Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results
The variance of the local density of the pair contact process with diffusion
(PCPD) is investigated in a bosonic description. At the critical point of the
absorbing phase transition (where the average particle number remains constant)
it is shown that for lattice dimension d>2 the variance exhibits a phase
transition: For high enough diffusion constants, it asymptotically approaches a
finite value, while for low diffusion constants the variance diverges
exponentially in time. This behavior appears also in the density correlation
function, implying that the correlation time is negative. Yet one has dynamical
scaling with a dynamical exponent calculated to be z=2.Comment: 20 pages, 5 figure
Quasi-normal modes of charged, dilaton black holes
In this paper we study the perturbations of the charged, dilaton black hole,
described by the solution of the low energy limit of the superstring action
found by Garfinkle, Horowitz and Strominger. We compute the complex frequencies
of the quasi-normal modes of this black hole, and compare the results with
those obtained for a Reissner-Nordstr\"{o}m and a Schwarzschild black hole. The
most remarkable feature which emerges from this study is that the presence of
the dilaton breaks the \emph{isospectrality} of axial and polar perturbations,
which characterizes both Schwarzschild and Reissner-Nordstr\"{o}m black holes.Comment: 15 pages, 5 figure
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
Integral Equations for Heat Kernel in Compound Media
By making use of the potentials of the heat conduction equation the integral
equations are derived which determine the heat kernel for the Laplace operator
in the case of compound media. In each of the media the parameter
acquires a certain constant value. At the interface of the media the
conditions are imposed which demand the continuity of the `temperature' and the
`heat flows'. The integration in the equations is spread out only over the
interface of the media. As a result the dimension of the initial problem is
reduced by 1. The perturbation series for the integral equations derived are
nothing else as the multiple scattering expansions for the relevant heat
kernels. Thus a rigorous derivation of these expansions is given. In the one
dimensional case the integral equations at hand are solved explicitly (Abel
equations) and the exact expressions for the regarding heat kernels are
obtained for diverse matching conditions. Derivation of the asymptotic
expansion of the integrated heat kernel for a compound media is considered by
making use of the perturbation series for the integral equations obtained. The
method proposed is also applicable to the configurations when the same medium
is divided, by a smooth compact surface, into internal and external regions, or
when only the region inside (or outside) this surface is considered with
appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into
the Reference List; a new section is added, a version that will be published
in J. Math. Phy
Extending Compositional Message Sequence Graphs
We extend the formal developments for message sequence charts (MSCs) to support scenarios with lost and found messages. We define a notion of extended compositional message sequence charts (ECMSCs) which subsumes the notion of compositional message sequence charts in expressive power but additionally allows to define lost and found messages explicitly. As usual, ECMSCs might be combined by means of choice and repetition towards (extended) compositional message sequence graphs. We show that - despite extended expressive power - model checking of monadic second-order logic (MSO) for this framework remains to be decidable. The key technique to achieve our results is to use an extended notion for linearizations
RNA polymerase motors: dwell time distribution, velocity and dynamical phases
Polymerization of RNA from a template DNA is carried out by a molecular
machine called RNA polymerase (RNAP). It also uses the template as a track on
which it moves as a motor utilizing chemical energy input. The time it spends
at each successive monomer of DNA is random; we derive the exact distribution
of these "dwell times" in our model. The inverse of the mean dwell time
satisfies a Michaelis-Menten-like equation and is also consistent with a
general formula derived earlier by Fisher and Kolomeisky for molecular motors
with unbranched mechano-chemical cycles. Often many RNAP motors move
simultaneously on the same track. Incorporating the steric interactions among
the RNAPs in our model, we also plot the three-dimensional phase diagram of our
model for RNAP traffic using an extremum current hypothesis.Comment: 6 pages, 7 figure
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