3,753,359 research outputs found
Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model
The -quantum group invariant spin 1/2 XXZ-Heisenberg model with open
boundary conditions is investigated by means of the Bethe ansatz. As is well
known, quantum groups for equal to a root of unity possess a finite number
of ``good'' representations with non-zero q-dimension and ``bad'' ones with
vanishing q-dimension. Correspondingly, the state space of an invariant
Heisenberg chain decomposes into ``good'' and ``bad'' states. A ``good'' state
may be described by a path of only ``good'' representations. It is shown that
the ``good'' states are given by all ``good'' Bethe ansatz solutions with roots
restricted to the first periodicity strip, i.e. only positive parity strings
(in the language of Takahashi) are allowed. Applying Bethe's string counting
technique completeness of the ``good'' Bethe states is proven, i.e. the same
number of states is found as the number of all restricted path's on the
-Bratteli diagram. It is the first time that a ``completeness" proof
for an anisotropic quantum invariant reduced Heisenberg model is performed.Comment: LaTeX file with LaTeX figures, 24 pages, 1 PiCTeX figur
Computation of the radiation amplitude of oscillons
The radiation loss of small amplitude oscillons (very long-living, spatially
localized, time dependent solutions) in one dimensional scalar field theories
is computed in the small-amplitude expansion analytically using matched
asymptotic series expansions and Borel summation. The amplitude of the
radiation is beyond all orders in perturbation theory and the method used has
been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our
results are in good agreement with those of long time numerical simulations of
oscillons.Comment: 22 pages, 9 figure
Short-time diffusion in concentrated bidisperse hard-sphere suspensions
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by
Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical
scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method
[Physica 120A, 388 (1983) & 126A, 349 (1984)]. Two species of hard spheres are
suspended in an overdamped viscous solvent that mediates the salient
hydrodynamic interactions among all particles. In a comprehensive parameter
scan that covers various packing fractions and suspension compositions, we
employ numerically accurate SD simulations to compute the initial diffusive
relaxation of density modulations at the Brownian time scale, quantified by the
partial hydrodynamic functions. A revised version of Beenakker and Mazur's
-scheme for monodisperse suspensions is found to exhibit
surprisingly good accuracy, when simple rescaling laws are invoked in its
application to mixtures. The so-modified scheme predicts
hydrodynamic functions in very good agreement with our SD simulation results,
for all densities from the very dilute limit up to packing fractions as high as
.Comment: 12 pages, 6 figure
Byzantine Gathering in Networks
This paper investigates an open problem introduced in [14]. Two or more
mobile agents start from different nodes of a network and have to accomplish
the task of gathering which consists in getting all together at the same node
at the same time. An adversary chooses the initial nodes of the agents and
assigns a different positive integer (called label) to each of them. Initially,
each agent knows its label but does not know the labels of the other agents or
their positions relative to its own. Agents move in synchronous rounds and can
communicate with each other only when located at the same node. Up to f of the
agents are Byzantine. A Byzantine agent can choose an arbitrary port when it
moves, can convey arbitrary information to other agents and can change its
label in every round, in particular by forging the label of another agent or by
creating a completely new one.
What is the minimum number M of good agents that guarantees deterministic
gathering of all of them, with termination?
We provide exact answers to this open problem by considering the case when
the agents initially know the size of the network and the case when they do
not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2.
More precisely, for networks of known size, we design a deterministic algorithm
gathering all good agents in any network provided that the number of good
agents is at least f+1. For networks of unknown size, we also design a
deterministic algorithm ensuring the gathering of all good agents in any
network but provided that the number of good agents is at least f+2. Both of
our algorithms are optimal in terms of required number of good agents, as each
of them perfectly matches the respective lower bound on M shown in [14], which
is of f+1 when the size of the network is known and of f+2 when it is unknown
Letter Written by Katherine Trickey to Her Folks Dated August 20, 1945
[Transcription begins]
Mon. P.M.
8.00 PM
20 Aug 45
Dear Folks,
Just a note before I go to the movies to see James Stewart in “Jimmy Steps Out.” We went on winter hours today 8 to 5.30 – Didn’t have to get up until 6.30 instead of 5.30 – Seemed good to me.
We had Sat off (all day) – washed & ironed until about 3 o’clock – then went to Macon for supper & the show – We (Marj, Minnie & I) saw Pan American – (which was pretty good).
Yesterday I slept nearly all day and read some – then went to the show last night – “Dangerous Partners” not really worth seeing.
This seems to be my show week! I even went Friday evening also! – and plan to go nearly every night this week as there are good shows every night!!
I’m afraid, Mother, that you’d better not make plans for my early return!! I don’t expect to be out for some time. Nothing yet has changed since the war ended. – I don’t think it will for some months.
This really is a rush job – I’ve got to finish now to get this mailed tonight!
Hastily but with love to all
Kay
[Transcription ends
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