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References
1
THOMPSON, G. H. B., and HENSHALL, G. D. : 'Nonradiative carrier loss
and temperature sensitivity of threshold in 1-27 jim
(GaIn)(AsP)/InP DH lasers', Electron. Lett., 1980,16, pp. 42-44
2
YANO, M., IMAI, H., and TAKUSAGAWA, M. : 'Analysis of threshold
temperature characteristics for InGaAsP/InP double heterojunction lasers', J. Appl. Phys., 1981, 52, pp. 3172-3175
3
OOMURA, E., MUROTANI, T., HIGUCHI, H., NAMIZAKI, H., a n d SUSAKI,
w.: 'Low threshold InGaAsP/InP buried crescent laser with
double current confinement structure', IEEE J. Quantum Electron.,
1981, QE-17, pp. 646-650
4
ISHIKAWA, H., IMAI, H., TANAHASHI, T., NISHITANI, Y., a n d TAKUSAGAWA, M.: 'V-grooved substrate buried heterostructure I n G a A s P -
/InP laser', Electron. Lett., 1981,17, pp. 465-466
5
MITO, I., KITAMURA, M., KAEDE, K., ODAGIRI, Y., SEKI, M., SUGIMOTO,
M., and KOBAYASHI, K.: 'InGaAsP planar buried heterostructure
laser diode (PBH-LD) with very low threshold current', ibid., 1982,
18, pp. 2-3
6
ADAMS, A. R., ASADA, M., SUEMATSU, Y., and ARAI, s.i T h e tem-
perature dependence of the efficiency and threshold current of
In^^Ga^As^P^y lasers related to intervalence band absorption',
Jpn. J. Appl. Phys., 1980,19, pp. L621-L624
0013-5194/82/160703-03$1.50/0
AUTOCORRELATION FUNCTION
PARAMETERS USED TO INDICATE
INCIPIENT BLOCKAGE IN A
PNEUMATIC TRANSPORT SYSTEM
Indexing terms: Measurement, Pneumatic transport, Stochastic processes
A study of autocorrelation properties in pneumatic transport
systems has been performed. The autocorrelation height at
zero time delay and the time delay at which the autocorrelation function becomes zero have been considered.
Introduction:
T h e use of pneumatic conveying for transporting
solids in pipelines is fairly well established. Conveyors have
been built involving many hundreds of metres of vertical lift
and horizontal pipeline runs. Both positive and negative pressure systems have been used, negative pressure systems having
the advantage of higher plant safety and cleanliness since all
leaks are inwards. Positive pressure systems, on the other
hand, allow a higher solids-mass flow rate since higher differential pressures can be established across the system. Indeed,
dense phase conveying (solids/air-mass flow-rate ratios of
> 20) can only be carried out under positive pressure. The
work described here concerns itself with light phase conveying
(solids/air-mass flow-rate ratio < 10). In this type of conveyor
the types of solids conveyed range from submicron cement
powder to 75 mm pieces of coal. Solids velocities range from 5
m/s to 50 m/s, and solids mass flow rates can be up to several
hundreds of tons per hour. Little if any automatic control of
these conveyors has been implemented to date.
In light phase conveying, degradation of solids and pipeline
wear are natural consequences of high-velocity pipeline transport. Also, the energy consumed per ton of solids transported
increases with increasing velocity (and also with decreasing
solids-mass flow rate). Fig. 1 shows a 3-D plot of air-mass
flow-rate against solids-mass flowrate against electrical energy
consumed by the compressor per kilogram of solids transported. As one would expect, the specific energy consumption
shows a strong dependency on the solids-mass flow rate.
There is also a minimum in specific energy consumption,
though less well pronounced, associated with the air-mass
flow rate for fixed solids-mass flow rate. Ideally, a pneumatic
conveyor should be run at as low a velocity and as high a
solids-mass flowrate as possible, thus minimising the aforementioned factors. However, at lower velocities the risk of
blocking the conveyor increases since for a given solids-mass
flow rate more solids reside in the conveyor than at higher
velocities. Clearly, in order to use the conveyor at the most
economic operating point, it is necessary to minimise the risk
of blockage and ensure that if the conveyor's operating conditions shift such that it is likely to block then some indication
of this is made or corrective action taken.
The crosscorrelation of two signals from transducers axially
spaced along a pipe will yield information on the velocity of
solids in the pipe,1 but this is not wholly indicative of incipient
pipeline blockage. Experiments have been performed using the
autocorrelation (ACF) function of the signal from one sensor,
and this seems to give much better indication of operation in
the region close to blockage of the pipe.
Experimental work: The experimental set-up at Bradford is a
negative-pressure pneumatic conveyor. The pipes, of 76 mm
ID aluminium, are in sections, facilitating the alteration of the
plant layout. A MINC-11 computer is used to monitor plant
performance, log measured data, and effect independent control over the air- and solids-mass flow rates (see Fig. 2). The
sensors used in the correlation work are ring sensors comprising a 2 mm-thick ring set flush to the pipe wall in PTFE
insulator. The charge induced in the ring is converted to a
voltage signal by a charge amplifier. The correlator used is a
Hewlett Packard 5420A digital signal analyser, this also being
controlled by the MINC-11 computer. The solids used for
these experiments were 3 mm PVC cubes. The MINC-11 was
programmed to set the solids-mass flow rate to five equally
spaced values in the range 0-12-0-67 kg/s. For each of these
values the air-mass flow rate was set to ten equally spaced
values in the range 0-1-0-22 kg/s. At each of these 50 operating points the correlator took and averaged a set of 50
autocorrelations each taken with 40 ms data time.
^air-mass flow rate.kg/s
Fig. 2 Schematic diagram of plant
Two parameters of the auto-correlation functions were
measured:
28
(a) the correlation height at zero time delay
(b) the time delay at which the ACF first became zero.
solids mass flow rate. kg/s
Fig. 1 Graph of air-mass flow rate against solids-mass flow rate against
energy consumption per kilogram of solids conveyed
ELECTRONICS LETTERS 5th August 1982
Vol.18
No. 16
These parameters were plotted as two 3-D graphs: solids-mass
flow rate against air-mass flow rate against correlation parameter (see Figs. 3 and 4).
705
At low solids-mass flow rates, the lines A-A' on the graphs,
the variation in ACF height is small over the whole range of
air-mass flow rates. Similarly the time delay for zero ACF
height shows little change. However, as we progress towards
high solids-mass flow rates, lines B-B' on the graph, we note
that the time delays exhibit a sharp upward trend at low air
velocities, with subsequent blockage of the conveyor as the
air-mass flow rate is decreased. The conveyor will operate for
an extended period at a point intermediate between the lower,
stable-running plateau and the upper, system-blocked plateau.
Acknowledgment: This work is financially supported by the
Science & Engineering Research Council, who has provided
grants for the equipment and research staff.
C. M. BECK
11th June 1982
R. M. HENRY
B. T. LOWE
A. PLASKOWSKI
Postgraduate School of Studies in Control Engineering
University of Bradford
Bradford, West Yorkshire BD7 1DP, England
References
1 BECK, M. s.: 'Cross-correlation flowmeters', NRDC Bull., 1981, 52,
p. 26
2
BENDAT, i. s., and PIERSOL, A. c : 'Measurement and analysis of
random data' (Wiley)
3
BECK, c. M., HENRY, R. M., LOWE, B. T., and PLASKOWSKI, A.: 'Instru-
mentation for minimising the operating costs of fluid transport
systems'. Interflow '82 Conference, Harrogate, 1982
0013-5194/82/160705-02$ 1.50/0
solids-mass"-flow rate,kg/s
Fig. 3 Graph of air-mass flow rate against solids-mass flow rate against
correlation zero time-delay height Rxx{0)
air-mass flow rate,kg/s
B1
SHORT CYCLING IN THE KRAVITZ-REED
PUBLIC KEY ENCRYPTION SYSTEM
Indexing terms: Codes, Polynomials
solids-mass flow rate,kg/s
Fig. 4 Graph of air-mass flow rate against solids-mass flow rate against
correlation time delay for zero height {Rxx( ) = 0)
On the ACF height graph another interesting feature develops at high solids loadings. As the air-mass flow rate is
dropped, the height of the correlation at zero time delay
(equivalent to the RMS voltage of the transducer output) falls,
but, at a point before system blockage occurs, the ACF rises
with decreasing air-mass flow rate and then continues to fall
again. This second peak in the ACF against air-mass flow rate
graph, which is more pronounced at high solids loadings, is a
repeatable indicator of conditions approaching blockage.
It should be possible to use these two properties of the ACF
as an indicator of the increased risk of system blockage with
decreasing air-mass flow rate or increasing solids-mass flow
rate. Measurement of the autocorrelation parameters at two
points along a pipeline and subtracting them should yield
information as to the operating trend of the conveyor (see Fig.
5). Stable flow should give zero difference, a trend towards
blockage, say, a positive difference and the opposite for a
trend away from blockage. The sharp rise in time delay for
zero ACF height suggests that it may be useful in switching
the control strategy of a pneumatic conveyor controller so as
to prevent the system from blocking while maintaining as
much as possible the constraints of minimum velocity and
maximum solids-mass flow rate and their associated benefits.
ACF
trend in solids-mass
flow rate along pipe
Fig. 5 Use of autocorrelations from two points along a pipeline to indicate the trend in solids-mass flow rate along the pipe
706
The Kravitz-Reed public key encryption system, a variant of
the MIT system based on Galois fields, is interesting because
it offers the potential of high security with efficient implementation. In the letter we demonstrate that high security
and efficient implementation are not, in reality, compatible
goals with this algorithm. Efficient implementation is subject
to a short cycling attack that exposes the secret key to computation. If the parameters of the algorithm are selected for
high security, then the algorithm cannot be efficiently implemented.
Description of algorithm: In the public key encryption system
introduced by Kravitz and Reed,1 an extension of the MIT
system,2 two irreducible polynomials, p(x) and q(x), having
degrees n and m, are selected. An enciphering exponent e relatively prime to r = (2" — lX2m — 1) is chosen; the deciphering
exponent d is the inverse of e modulo r. A message y is enciphered as E(y) = ye mod /, where f(x) = p{x)q(x). The ciphertext E{y) is decrypted using the same formula with d replacing e. Kravitz and Reed base the security of this algorithm on
the supposition that one must factor the polynomial f(x) in
order to discover n and m, and thus the secret key d, from the
public key (e,/). However, it appears that a short cycling
attack based on superenciphering any polynomial with enciphering exponent e = any power of 2 will provide the values
of n and m with work factor nm. Here we note that efficient
hardware implementations rest on selecting n and m to have
perhaps 3 to 5 decimal digits, which would lead to shift register implementations involving several hundred to a few thousand bits. Unfortunately this selection of n and m leads to a
work factor for penetration of about 103 to 105 encryption
operations, which is trivial. Proper security will require that n
and m be selected to have several hundred decimal digits,
which will prejudice efficient implementations.
Short cycling: Short cycling attacks against other public key
algorithms3-4 have proved to be largely unsuccessful, possibly
because the attempts may have been too limited by concentrating on the received ciphertext while trying to recover
plaintext. When applied in this way the short cycling attack is
generally little better than using the algorithm as a randomnumber generator. In using short cycling to attack the
Kravitz-Reed algorithm, however, we ignore intercepted ciphertext, and instead concentrate on recovering n and m from
knowledge of/(x) only.
ELECTRONICS LETTERS 5th August 1982 Vol. 18 No. 16
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