## Elmer Tory

Professor emeritus

### Contact Information

- elmer@sherpasoftware.ca
- Phone
- (506) 536-2426
- Office
- Office hours
- Other websites

Contact

36 Queens Road

P. O. Box 6054, Sackville, NB, E4L 1G6

Phone: (506) 536-2426

### Education

Bachelor of Science (Honours Chemistry), University of Alberta

Ph. D. (Chemical Engineering), Purdue University

### Research interests

### Publications

Books

E.
M. Tory (ed.). *Sedimentation of Small Particles in a Viscous Fluid*,
Computational Mechanics Publications, Southampton, UK (1996).

M.
C. Bustos, F. Concha, R. Bürger, and E. M. Tory. *Sedimentation and
Thickening. Phenomenological Foundation and Mathematical Theory*. Kluwer
Academic Publishers, Dordrecht (1999).

Thesis

E.
M. Tory. *Batch and continuous thickening*. Ph. D. thesis, Purdue University, June, 1961.

Papers

93.
Monika Bargiel and Elmer M. Tory. Solution of Linear and Nonlinear Diffusion
Problems via Stochastic Differential Equations, Computer Science **16**, 415-428 (2015).

92.
Monika Bargiel and Elmer M. Tory. Effect of higher-order and lubrication terms
on the stability of polygonal
arrangements of sedimenting spheres, Powder Technology** 264**, 519-526 (2014).

91.
Monika Bargiel and Elmer M. Tory. Extension of the Richardson-Zaki equation to
suspensions of multisized irregular particles, Int. J. Mineral Processing **120**, 22-25 (2013).

90.
Monika Bargiel, Merzik T. Kamel, and Elmer M. Tory. Periodic motion of four
spheres in a "kite" configuration, Powder Technology **214**, 14-20 (2011).

89.
Stefan Berres, Ricardo Ruiz-Baier, Helmut Schwandt, and Elmer M. Tory. An
adaptive finite-volume method for a model of two-phase pedestrian flow, Networks and Heterogeneous Media **6**, 401-423 (2011).

88. Stefan Berres,
Ricardo Ruiz-Baier, Helmut Schwandt, and Elmer M. Tory. Two-dimensional model
of pedestrian flow, P.G. Ciaret and Ta-Tsien Li, Eds. *Series in Contemporary Applied Mathematics* (*Proceedings of HYP2010*),
Higher Education Press (Beijing) and World Scientific (Singapore) 2011.

** **

87.
F. Betancourt, R. Bürger, K.H. Karlsen, and E.M. Tory. On nonlocal conservation
laws modelling sedimentation, *Nonlinearity***24**, 855-885 (2011).

86.
Monika Bargiel and Elmer M. Tory. A comparison of the results of two methods
for computing the sedimentation behavior of bidisperse suspensions, *Int. J. Mineral Processing*, **95**, 53-61 (2010).

85. Monika Bargiel and Elmer M. Tory. A particle-based approach to sedimentation and fluidization. In Leading-Edge Applied Mathematical Modeling Research, Matias P. Alvarez (ed), Nova Science Publishers, 2008, pp 19-65.

84.
Monika Bargiel and Elmer M. Tory.** **A five-parameter
Markov model for simulating the paths of sedimenting particles, *Appl. Math. Modelling ***31**, 2080-2094 (2007).

83.
Monika Bargiel and Elmer M. Tory. Stability of tridisperse suspensions, *Computing and Visualization in Sci*. **10**, 163-170 (2007).

** **

82.
Monika Bargiel and Elmer M. Tory. Simulation of sedimentation and fluidization
of polydisperse suspensions via a Markov
model, *Chem. Eng. Sci*. **61**, 5575-5589 (2006).

81.
Monika Bargiel and Elmer M. Tory. An extension of the particle-based approach
to simulating the sedimentation of polydisperse suspensions, *Int. J. Mineral Processing ***79** 235-252 (2006).

80.
Stefan Berres, Raimund Bürger and Elmer M. Tory. Applications of polydisperse
sedimentation models, *Chem. Eng. Journal*, **111, **105-117 (2005).

79.
Monika Bargiel, Robert A. Ford and Elmer M. Tory. Simulation of sedimentation of
polydisperse suspensions: a particle-based approach, *AIChE Journal*, **51**,
2457-2468 (2005).

78.
Stefan Berres, Raimund Bürger and Elmer M. Tory. On mathematical models and
numerical simulation of the fluidization of polydisperse suspensions, *Applied Math. Modelling*, **29**, 159-193 (2005).

77.
S. Berres, R. Bürger, and E. M. Tory. Mathematical model and numerical
simulation of the liquid fluidization of polydisperse solid particle mixtures, *Computing and Visualization in Sci*. **6**, 67-74 (2004).

76.
E. M. Tory and R. A. Ford. Simulation of sedimentation of bidisperse
suspensions. *Int. J. Mineral Processing ***73**, 119-130 (2004).

75.
Stefan Berres, Raimund Bürger, Kenneth H. Karlsen and Elmer M. Tory. Strongly
degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation
with compression,* SIAM J. Appl. Math.***64**, 41-80 (2003).

74.
Stefan Berres, Raimund Bürger and Elmer M. Tory. Mixed-type systems of
convection-diffusion equations modeling polydisperse sedimentation,* *In *Analysis
and Simulation of Multifield Problems*, M.A. Efandiev and W.L. Wendland
(Eds.)*, Lecture Notes in Applied and
Computational Mechanics*, Vol. 12, Springer-Verlag, 2003, pp 257-262.

73.
E. M. Tory, R. A. Ford and M. Bargiel. Simulation of sedimentation of
monodisperse and polydisperse suspensions, *Analysis
and Simulation of Multifield Problems,* M.A. Efandiev and W.L. Wendland
(Eds.)*, Lecture Notes in Applied and
Computational Mechanics*, Vol. 12, Springer-Verlag, 2003, pp 343-348.

72.
R. Bürger, K. H. Karlsen, E. M. Tory, and W. L. Wendland. Model equations and
instability regions for the sedimentation of polydisperse suspensions of
spheres. *Z. Angew. Math. Mech.* **82**, 699-722 (2002).

71.
M. Bargiel and E. M. Tory. Packing fraction and measures of disorder of
ultradense packings of equal spheres. II. Transition from dense random packing.
*Advanced Powder Technol.* **12**, 533-557 (2001).

70.
E. M. Tory and R. A. Ford. Stochastic simulation of sedimentation. In *Advances
in Fluid Mechanics III*, M. Rahman and C. A. Brebbia (Eds.). WIT Press
(2000), pp. 663-672.

69.
E. M. Tory. Stochastic sedimentation and hydrodynamic diffusion. *Chemical
Engineering Journal ***80**, 81-89 (2000).

68.
R. Bürger and E. M. Tory. On upper rarefaction waves in batch settling.*
Powder Technol.***108**, 74-87 (2000).

67.
E. M. Tory and M. T. Kamel. Mean velocities in polydisperse suspensions. *Powder
Technol.*** 93**, 199-207 (1997).

66.
M. Bargiel and E. M. Tory. Stochastic dynamic solution of nonlinear
differential equations for transport phenomena. *AIChE Journal* **42**,
889-891 (1996).

65.
E. M. Tory and C. H. Hesse. Experimental evidence for a Markov model for
sedimentation. In *Sedimentation of Small Particles in a Viscous Fluid*,
E. M. Tory (ed.), Computational Mechanics Publications, Southampton, UK (1996),
pp. 241-281.

64.
C. H. Hesse and E. M. Tory. The stochastics of sedimentation. In *Sedimentation
of Small Particles in a Viscous Fluid*, E. M. Tory (ed.), Computational
Mechanics Publications, Southampton, UK (1996), pp. 199-239.

63.
E. M. Tory, R. J. Hughes, and M. Bargiel. Validity of measures of sedimentation
velocity. *Powder Technol.*** 84**, 259-267 (1995).

62.
E. M. Tory, M. Bargiel, and R.L. Honeycutt. A three-parameter Markov model for
sedimentation III. A stochastic Runge-Kutta method for computing first-passage
times. *Powder Technol.*** 80**, 133-146 (1994).

61.
E. M. Tory. The complex behaviour of simple systems of sedimenting spheres. *Proc.
Atlantic Math. Days*, L. E. Garey and M. H. Hamdan (eds.), Univ. New
Brunswick, Saint John, NB, Oct. 29-30, 1993. Reprinted in *The Blundon
Lectures, 1982-1997*, R. Turner (ed.), UNB, 1997, pp. 105-110

60.
M. Bargiel and E. M. Tory. Packing fraction and measures of disorder of
ultradense packings of equal spheres. I. Nearly ordered packing. *Advanced
Powder Technol.* **4**, 79-101 (1993).

59.
E. M. Tory, M. Bargiel, and M. T. Kamel. The distribution of velocities of a
concentric sphere in a dispersion of spheres sedimenting in a spherical
container. *Powder Technol.*** 74**, 159-169 (1993). Erratum. *ibid.***94**, 267 (1997).

58.
E. M. Tory, M. T. Kamel, and C. F. Chan Man Fong. Sedimentation is
container-size dependent. *Powder Technol.*** 73**, 219-238 (1992).

57.
E. M. Tory and M. T. Kamel. A note on the periodic motion of four spheres. *Powder
Technol.*** 73**, 95-96 (1992).

56.
E. M. Tory and D. K. Pickard. Unilateral Gaussian Fields. *Advances in Appl.
Prob.* **24**, 95-112 (1992).

55.E. M. Tory, M. T. Kamel, and C. B. Tory. Sedimentation of clusters of
identical spheres III. Periodic motion of four spheres.* Powder Technol.***
67**, 71-82 (1991).

54.
M. T. Kamel and E. M. Tory. Sedimentation of clusters of identical spheres II.
Periodic motion of three spheres.* Powder Technol.*** 63**, 187-195
(1990).

53.
M. Bargiel and E. Tory. Simulation of homogeneous isotropic transitional
packings of equal spheres. *Proc. 2 ^{nd} World Congress Particle
Technology*, Kyoto, Sept. 19-22, 1990, Part I, pp. 142-149.

52.
E. M. Tory. A stochastic model for the slow sedimentation of small particles in
a viscous fluid. In *Ocean Waves Mechanics, Computational Fluid Dynamics and
Mathematical Modelling,* M. Rahman (ed.), Computational Mechanics
Publications, Boston, 1990, pp. 671-685.

51.
M. T. Kamel and E. M. Tory. Sedimentation of clusters of identical spheres I.
Comparison of methods for computing velocities. *Powder Technol.*** 59**,
227-248 (1989). Erratum. *ibid.* **94**, 266 (1997).

50.
E. M. Tory and D. K. Pickard. A stochastic analysis of a new fixed-distance
experiment in sedimentation. In *Continuum Mechanics and its Applications*,
G. A. C. Graham and S. K. Malik (eds.), Hemisphere, New York, 1989, pp. 289-298.

49.
E. M. Tory and M. T. Kamel. On the divergence problem in calculating particle
velocities in dilute dispersions of identical spheres III. Sedimentation in a
spherical container. *Powder Technol.*** 55**, 187-192 (1988).

48.
E. M. Tory and M. T. Kamel. On the divergence problem in calculating particle
velocities in dilute dispersions of identical spheres II. Effect of a plane
wall. *Powder Technol.*** 55**, 51-59 (1988). Erratum. *ibid.* **94**,
265 (1997).

47.
D. K. Pickard, E. M. Tory, and B. A. Tuckman. A three-parameter Markov model
for sedimentation II. Simulation of transit times and comparison with
experimental results. *Powder Technol.*** 49**, 227-240 (1987).

46.
D. K. Pickard and E. M. Tory. A Markov model for sedimentation: Fundamental
issues and insights. In *Advances in the Statistical Sciences*, Vol. IV,
Stochastic Hydrology, I. B. MacNeill and G. J. Umphrey (eds.), D. Reidell,
Dordrecht, 1987, pp. 1-25.

45.
E. M. Tory and D. K. Pickard. On the divergence problem in calculating particle
velocities in dilute dispersions of identical spheres. *Powder Technol.***
47**, 39-42 (1986). Corrigenda, *ibid*. **48**, 189 (1986).

44.
E. M. Tory and D. K. Pickard. Experimental evidence for a stochastic approach
to sedimentation. In *Flocculation, Sedimentation and Consolidation*, B.
M. Moudgil and P. Somasundaran (eds.), AIChE, New York, 1986, pp 297-306.

43.
D. K. Pickard, B. A. Tuckman, and E. M. Tory. Experimental evidence for a
three-parameter Markov model for sedimentation: Simulation and analysis of
transit times for spheres in monodisperse suspensions. *Proc. 1 ^{st}
World Congress Particle Technology*, Nürnberg, April 16-18, 1986, Part IV,
pp. 325-339.

42.
E. M. Tory, C. B. Yhap, and D. K. Pickard. Periodicity and fine structure in
two-dimensional gravitational random packing.* Particulate Sci. and Technol. ***3**,
89-99 (1985).

41.
W. S. Jodrey and E. M. Tory. Computer simulation of close random packing of
equal spheres. *Phys. Rev. A* **32**, 2347-2351 (1985). Erratum. *ibid.***34**, 675 (1986).

40.
D. K. Pickard and E. M. Tory. Simulation of sedimentation, Stochastic
Hydrology, Applied Probability in Biology and Engineering, Adv. Appl. Prob. **16**, 22 (1984).

39.
E. M. Tory and D. K. Pickard. Sedimentation of slurries: the long and winding
road to chaos. *Proc. Atlantic Math Days*, Fredericton, NB, Oct. 28-29,
1983. University of New Brunswick, May 1984, pp. 84-96.

38.
E. M. Tory and W. S. Jodrey. Comments on some types of random packing. In *Advances
in the Mechanics and The Flow of Granular Materials.* M. Shahinpoor (ed.),
Trans Tech Publications, Vol. 1, pp 75-106 (1983).

37.
E. M. Tory, W. S. Jodrey, and D. K. Pickard. Simulation of random sequential
adsorption: efficient methods and resolution of conflicting results. *J.
Theor. Biol.* **102**, 439-445 (1983).

36.
E. M. Tory and D. K. Pickard. Extensions and refinements of a Markov model for
sedimentation. *J. Math. Anal. Appl.* **86**, 442-470 (1982).

35.W. S. Jodrey and E. M. Tory. Computer simulation of isotropic, homogeneous,
dense random packing of equal spheres. *Powder Technol.*** 30**,
111-118 (1981).

34.
E. M. Tory and D. K. Pickard. A resolution of the disparity between interface
velocities and mean velocities in cluster settling. *Proc. 2 ^{nd}
World Congress Chem. Eng.*, Montreal, Oct. 4-9, 1981, Vol. 5, pp. 254-257.

33.
E. M. Tory and D. K. Pickard. An application of mixture theory to particulate
sedimentation. *ASME J. Appl. Mech. ***48**, 210 (1981).

32.
D. K. Pickard and E. M. Tory. A critique of Weiner’s work on Palasti’s
conjecture. *J. Appl. Prob.* **17**, 880-884 (1980).

31.
W. S. Jodrey and E. M. Tory. Random sequential packing in *R ^{n}*,

*J. Stat. Comp. Simulation*

**10**, 87-94 (1980).

30.
D. K. Pickard and E. M. Tory. Experimental implications of a Markov model for
sedimentation. *J. Math. Anal. Appl.* **72**, 150-176 (1979).

29.
E. M. Tory and D. K. Pickard. Some comments on “Sequential random packing in
the plane” by H. J. Weiner. *J. Appl .Prob. ***16**, 699-702 (1979).

28.
M. T. Kamel, E. M. Tory, and W. S. Jodrey. The distribution of *k*th
nearest neighbours and its application to cluster settling in dispersions of
equal spheres. *Powder Technol.*** 24**, 19-34 (1979).

27.
D. K. Pickard and E. M. Tory. The radial distribution of hard rods. *J. Chem.
Phys.*** 70**, 5923 (1979).

26.
M. T. Kamel, P. N. Kaloni, and E. M. Tory. Two-dimensional internal flows of
polar fluids. *J. Rheology*** 23**, 141-150 (1979).

25.
W. S. Jodrey and E. M. Tory. Simulation of random packing of spheres. *Simulation***32**, 1-12 (1979).

24.
K. Gotoh, W. S. Jodrey, and E. M. Tory. Average nearest-neighbour spacing in a
random dispersion of equal spheres. *Powder Technol.*** 21**, 285-287
(1978).

23.
E. M. Tory, J. W. Mosevich, and V. M. Reddy. A technique for the determination
of the concentration distribution in a sedimenting suspension via radioactive
solids. *Can. J. Chem. Eng. ***56**, 472-477 (1978). Errata *ibid. ***57**,
121 (1979).

22.
K. Gotoh, W. S. Jodrey, and E. M. Tory. Variation in the local packing density
near the wall of a randomly packed bed of equal spheres. *Powder Technol.***
20**, 257-260 (1978).

21.
K. Gotoh, W. S. Jodrey, and E. M. Tory. A random packing structure of equal
spheres – statistical geometrical analysis of tetrahedral configurations. *Powder
Technol.*** 20**, 233-242 (1978).

20.
E. M. Tory and D. K. Pickard. A three-parameter Markov model for sedimentation.
*Can. J. Chem. Eng. ***55**, 655-665 (1977).

19.
D. K. Pickard and E. M. Tory. A Markov model for sedimentation. *J. Math.
Anal. Appl.* **60**, 349-369 (1977).

18.
J. R. Smith and E. M. Tory. Unsteady viscometric flow. *Can. J. Chem. Eng. ***51**,
642-646 (1973).** **

17.
E. M. Tory, B. H. Church, M. K. Tam, and M. Ratner. Simulated random packing of
equal spheres. *Can. J. Chem. Eng. ***51**, 484-493 (1973). Errata. *ibid.
***51**, 622 (1973).

16.
E. M. Tory. Continuous thermal diffusion. *Chem. Eng. Sci.* **27**,
1194 (1972).

15.
E. M. Tory. A simple representation of polyadic harmonics and their inner
products with other polyadics. *Chem. Eng. Sci. ***24**, 1637-1639
(1969).

14.
E. M. Tory, N. A. Cochrane, and S. R. Waddell. Anisotropy in simulated packing
of equal spheres. *Nature* **220**, 1023-1024 (1968).

13.
E. M. Tory. Discussions and contributions (Papers by C. C. Dell and J. Sinha,
and K. Scott and J. L. Alderton. *Trans. Instn Min. Metall. (Section C:
Mineral Process. Extr. Metall.)*** 76**, C139-C140 (1967).

12.
E. M. Tory and D. Hum. Correspondence. New optimization method is highly
suitable for chemical engineering applications. *Can. J. Chem. Eng.* **45**,
119 (1967).

11.
P. T. Shannon and E. M. Tory. The analysis of continuous thickening. *SME
Trans.* **235**, 375-382 (1966).

10.
R. J. Wheeler and E. M. Tory. *Volume-density relationships and their use in
the study and prevention of kinematic waves in traffic*. Department of
Highways, Ontario, Report RB112, June, 1966.

** **

9.
E. M. Tory and P. T. Shannon. Subsidence of slimes. *J. Colloid &
Interface Science ***21**, 107-109 (1966).

8.
P. T. Shannon and E. M. Tory. Correspondence. Batch and continuous thickening.
Prediction of batch settling behavior with results for rigid spheres. *Ind.
Eng. Chem. Fundamentals ***4**, 367-368 (1965).

** **

7.
R. J. Wheeler and E. M. Tory. The use of the flux plot in traffic control. *Traffic
Quarterly* **19**, 369-383 (1965).

6.
E. M. Tory and P. T. Shannon. A reappraisal of the concept of settling in
compression. Settling behavior and concentration profiles for initially
concentrated calcium carbonate slurries.* Ind. Eng. Chem. Fundamentals ***4**,
194-204 (1965).

5.
P. T. Shannon and E. M. Tory. Settling of slurries – new light on an old
operation. *Ind. Eng. Chem. ***57 (2)** 18-25 (1965).

4.
E. M. Tory. Absence of concentration gradients in slurries settling at high
Reynolds numbers. *Ind. Eng. Chem. Fundamentals ***4**, 106-107 (1965).

3.
P. T. Shannon, R. D. DeHaas, E. P. Stroupe, and E. M. Tory. Batch and
continuous thickening. Prediction of batch settling behavior with results for
rigid spheres. *Ind. Eng. Chem. Fundamentals ***3**, 250-260 (1964).

2.
P. T. Shannon, E. Stroupe, and E. M. Tory. Batch and continuous thickening.
Basic theory. Solids flux for rigid spheres. *Ind. Eng. Chem. Fundamentals ***2**,
203-211 (1963). Correction. *ibid.* **3**, 184 (1964).

1.
W. J. Brickman, H. B. Dunford, E. M. Tory, J. L. Morrison, and R. K. Brown. The
reactivity of cellulose II. Water sorption, heats of wetting, and the reactions
with thallous ethylate in ether, nitration mixtures, and heavy water of cotton
linters alternately wetted with water and dried. *Can. J. Chem. ***31**,
550-563 (1953).