Student Research Projects
Suggestions for Student Research Projects
Good journal sources for ideas include Computers in Physics (now
Computing in Science and Engineering), Physical Review
Letters, Physica, Physical
Review B, and Physical Review E, Chaos, the Journal of Chemical Physics. In the following we
list some suggestions that we have found in the recent research
literature. You can use the Edit menu or press the
Find button in the toolbar to search for keywords.
Physical Review E
- F. Cecconi, R. Livi, and A. Politti, "Fuzzy transition region
in a one-dimensional coupled-stable-map lattice," Phys. Rev. E 57,
2703 (1998).
- Jean-Pierre Goedgebuer, Laurent Larger, and Henri Porte,
"Chaos in wavelength with a feedback tunable laser diode," Phys. Rev.
E 57, 2795 (1998).
- Bing-Hong Wang, Yvonne-Roamy Kwong, and Pak-Ming Hui,
"Statistical mechanical approach to Fukui-Ishibashi traffic flow
models," Phys. Rev. E 57, 2568 (1998).
- G. Berkolaiko and S. Havlin, "Number of distinct sites visited
by Levy flights injected into a d-dimensional lattice," Phys. Rev. E
57, 2549 (1998).
- A. Venkatesan and M. Lakshmanan, "Bifurcation and chaos in the
double-well Duffing-van der Pil oscillator: Numerical and analytical
studies," Phys. Rev. E 56, 6321 (1997). keyword: Runge-Kutta.
- E. Ben-Naim and P. L. Krapivsky, "Stationary velocity
distributions in traffic flows," Phys. Rev. E 56, 6680 (1997).
Their model incorporates clustering and passing. They show real
data for a rural road.
- Zbigniew Koza and Haim Taitelbaum, "Reaction-diffusion front
in a system with strong quenched disorder," Phys. Rev. E 56,
6387 (1997). keyword: Sinai disorder.
- T. T. Rautiainen, M. J. Alava, and K. Kaski, "Dynamics of
fracture in dissipative systems," Phys. Rev. E 56, (1997).
keyword: crack.
- Sang-Yoon Kim, Seung-Ho Shin, Jaichul Yi, and Chi-Woong Jang,
Bifurcations in a parametrically forced magnetic pendulum," Phys.
Rev. E 56, 6613 (1997). keyword: Floquet theory.
- Ezequiel V. Albano, "Properties of the interface generated by
the collision of two growing interfaces," Phys. Rev. E 56,
7301 (1997).
- Claus Wilke and Thomas Martinetz, "Simple model of evolution
with variable system size," Phys. Rev. E 56, 7128 (1997).
- Maxim Vergeles, Pawel Keblinski, Joel Koplik, and Jayanth R.
Banavar, "Stokes drag and lubrication flows: A molecular dynamics
study," Phys. Rev. E 53, 4852 (1996).
- Jeffrey L. Rogers and Luc T. Wille, "Phase transitions in
nonlinear oscillator chains," Phys. Rev. E 54, R2193 (1996). A
good example of a phase transition from a synchronized to a
desynchronized state as the interaction of interaction is decreased.
Fourth-order Runge-Kutta is used.
- Lech Longa, Evaldo M. F. Curado, and Fernando A. Oliveira,
"Roundoff-induced coalescence of chaotic trajectories," Phys. Rev. E
54, R2201 (1996). The authors consider the logistic map with
noise.
- D. R. M. Williams and F. C. MacKintosh, "Driven granular media
in one dimension: correlations and equation of state," Phys. Rev. E
54, R9 (1996). From Fred MacKintosh: Imagine a plate
containing macroscopic particles that collide inelastically, and that
are driven by vibrations of the plate. In addition to the individual
collision processes, each particle executes a random walk in
velocity. What is actually done for speed in the simulation is to
determine when collisions will occur, then update the velocities
according to their eq. (2). Hence they do not really use a fixed time
step.
- A. Malthe-Sorenssen, "Kinetic grain model for sandpiles,"
Phys. Rev. E 54, 2261 (1996). Another sandpile model.
- Maksim N. Stolyarov, Victor A. Romanov, and Evgenii I. Volkov,
"Out-of-phase mixed-mode oscillations of two strongly coupled
identical relaxation oscillators," Phys. Rev. E 54, 163 (1996). keyword: biological membranes.
- Concepcion Tojo and Panos Argyrakis, "Correlation random walk
in continuous space," Phys. Rev. E 54, 58 (1996). The model
consists of a random walk in two dimensions. The length of each step
is constant. The angle of each step is a continuous function. A
maximum angle theta is introduced. The direction of the next step is
chosen at random in the interval -q/2 to FONT FACE="symbol">+q
/2 relative to the
previous step thus introducing some directional memory. The usual
asymptotic results are obtained, but crossover effects are observed.
Maksim N. Stolyarov, Victor A.
Romanov, and Evgenii I. Volkov, "Out of phase mixed mode oscillations of two strongly coupled
identical relaxation oscillators," Phys. Rev. E 54, 163 (1996).
They solve a system of two coupled differential equations which
describe liquid peroxidation in biological membranes. The 4th-order
Runge Kutta method with variable step size is used. The results are
compared with the Brusselator oscillator.
Tong Zhou and Lep P.
Kadanoff, "Inelastic collapse of three particles," Phys. Rev. E 54, 623 (1996). Most of the results are
analytical, but the results are checked by simulations. A good
supplement to the one-dimensional case.
Riccardo Simonazzi and Alexander Tenenbaum, "Anomalous fluctuations in low temperature molecular dynamics
simulations," Phys. Rev.
E 54, 964 (1996). A constant energy molecular dynamics
simulation of a solid at low temperature is found to be only weakly
chaotic. The reason is that the system acts like a system of coupled
oscillators with a small anharmonic potential.
Imre Derenyi and Armand Ajdari, "Collective transport of particles in a 'flashing' periodic
potential," Phys. Rev. E 54,
R5 (1996). The motivation of this study is to understand the motion
of motor proteins. The one-dimensional dynamics of a particle is
given by the Langevin equation with the constraint that the neighbor
particles are not allowed to overlap. The external potential is
spatially periodic in is turned on and off periodically.
Patrici Molinas-Mata, M. A. Munoz,
Daniel O. Martinez, and Albert-Laszlo Barabasi, "Ballistic random walker," Phys. Rev. E
54, 968 (1996). A random walker moves in a straight line until
reaches a previously unvisited site at which it changes direction
randomly. What is the asymptotic time-dependence of the mean-square
displacement?
Kai Nagel, "Particle hopping models and traffic flow theory,"
Phys. Rev. E 53, 4655 (1996).
Weiguang Huang and D. Brynn
Hibbert, "Computer modeling of electrochemical growth with convection
and migration in a rectangular cell," Phys. Rev. E 53, 727-730 (1996). The authors develop
differential equations for modeling the growth of electrodeposits by
diffusion, convection, and migration in an electric field. The
pattern formations in a two-dimensional rectangular cell are found by
doing computer simulations on a personal computer.
M. Wittkop, S.
Kreitmeier, and D. Goumlritz, "Monte Carlo simulations of a single polymer chain under
extension above and below the theta temperature," Phys. Rev. E 53, 838-845 (1996).
A good summary of the types of simulations that are possible for
investigating the elastic properties of polymers. The simulations are
too time consuming for most student projects.
Sandra J. Barsky and Michael Plischke, "Order and localization in randomly cross-linked polymer
networks," Phys. Rev. E
53, 871--876 (1996). See the related article by K. Kremer and
G. S. Grest in Monte Carlo and Molecular Dynamics Simulations in
Polymer Science, edited by K. Binder, Clarendon Press (1994).
Liv Furuberg, Knut
Joslashrgen Maloslashy, and Jens Feder, "Intermittent behavior in slow drainage," Phys. Rev. E 53,
966-977 (1996). The authors discuss a variation of the invasion
percolation algorithm.
Shuji Ogata, "Direct Monte Carlo sampling of the short-range screening
potentials for classical Coulomb liquids," Phys. Rev. E
53, 1094-1099 (1996). The author introduces a fictitious
attractive interaction to sample the radial distribution function
g(r) more efficiently for small r. The method is a good example of
important sampling.
Robert L. Leheny, "Simple model for river network evolution,"
Phys. Rev. E 52, 5610 (1995). This model is discussed in
Chapter 19 of our computer
simulation text.
Xingzhi Zhang
and Gang Hu, "1/f noise in a two-lane highway traffic model," Phys. Rev. E 52, 4664-4668 (1995). One of many
recent articles on modeling traffic flow.
P. S.
Landa and M. G. Rosenblum, "Modified Mackey-Glass model of respiration control," Phys. Rev. E 52, R36 (1995). Such
models look like a good way of introducing science majors to the
human respiratory system.
A. M. Albano, P. E. Rapp, and A. Passamante, "Kolmogorov-Smirnov test distinguishes attractors with similar
dimensions," Phys. Rev.
E 52, 196 (1995). A clearly written paper which uses the
correlation integral.
Atsuhiko Maeda and Toyonori Munakata, "Lattice thermal conductivity via homogeneous nonequilibrium
molecular dynamics," Phys. Rev.
E 52, 234 (1995). The method is applied to a one-dimensional
anharmonic lattice.
Nigel B. Wilding, "Critical-point and coexistence-curve properties of the
Lennard-Jones liquid," Phys. Rev. E 52, 602
(1995). Uses advanced Monte Carlo methods, but the application is
very clear.
T. J. P. Penna et
al., "Long-range anticorrelations and non-Gaussian behavior of a
leaky faucet," Phys. Rev. E 52, R2168 (1995). A model of a dripping
faucet based on the near and next-nearest Ising model is analyzed.
I. M. Kyprianidis et al., "Crisis-induced intermittency in a third-order electrical
circuit," Phys. Rev. E 52, R2268
(1995). A relatively simple electrical circuit is analyzed and
simulated.
Brad Lee Holian et al., "Thermostatted molecular dynamics: How to avoid the Toda demon
hidden in Nose-Hoover dynamics," Phys. Rev. E
52, R2338 (1995). The authors discuss a method for doing
constant temperature molecular dynamics.
Ch. Dellago and H. A. Posch, "Lyapunov exponents of systems with elastic hard collisions,"
Phys. Rev.
E 52, 2401 (1995). The authors compute the maximum Lyapunov
exponent for the two-dimensional Lorentz gas and for the stadium
billiard.
Eric Bonabeau and Laurent Dagorn, "Possible universality in the size distribution of fish
schools," Phys. Rev. E 51,
R5220-R5223 (1995). It is observed that N(s), the frequency of fish
schools of size s, follows a power law, s-3/2 up to a
cutoff size. The authors discuss a model that yields similar results.
Assume that there are N sites in which n fish move; r fish swimming
together form a r-school. At each time step, all schools move to a
randomly selected site (which can be anywhere in the lattice. If a
r-school and a s-school land at the same site, they form a
(r+s)-school.
Griggory V. Osipov, Arkady S. Pikovsky, Michael
G. Rosenblum, and Jurgen Kurths, "Phase synchronization effects in a lattice of nonidentical
Rossler oscillators," Phys. Rev. E 55, 2353 (1997).
A simple model for introducing the concept of phase synchronization.
S. Clar, K.
Schenk, and F. Schwabl, "Phase transitions in a forest-fire model," Phys. Rev. E 55, 2174 (1997). The
density of empty sites is assumed to be a constant. Interesting
behavior is found.
D. A. Head and G. J. Rodgers, "Crossover to self-organized criticality in an inertial
sandpile model," Phys. Rev. E
55, 2573 (1997). The authors incorporate inertia in a
one-dimensional model and discuss simulations and mean-field results.
Tohru Ikeguchi and
Kazuyuki Aihara, "Difference correlation can distinguish deterministic chaos
from 1/fand-type colored noise," Phys. Rev. E 55, 2530 (1997). The authors
consider the power spectra of the Henon, Ikeda, and Bernoulli maps
and data sets from the Santa Fe Institute Time Series Prediction
Competition.
George G. Szpiro, "Forecasting chaotic time series with genetic algorithms,"
Phys. Rev. E 55, 2557 (1997).
Toru Ohira and
Ryusuke Sawatari, "Delay estimation from noisy time series," Phys. Rev. E 55, R2077 (1997).
Physical Review Letters
- Rolando Castro and Tim Sauer, "Chaotic Stochastic Resonance:
Noise-Enhanced reconstruction of Attractors," Phys. Rev. Lett. 79,
1030 (1997).
- Surajit Sen, Robert S. Sinkovits, and Soumya
Chakravarti, "Algebraic Relaxation Laws for Classical Particles in 1D
Anharmonic Potentials," Phys. Rev. Lett. 77, 4855 (1996).
- Frank-Michael Dittes, "Optimization on rugged landscapes: a new general purpose
Monte Carlo approach," Phys. Rev. Lett.
76, 4651 (1996). The applications to the N-k model, the
Coulomb glass, and the traveling salesman problem are accessible and
impressive.
- Guido Caldarelli, Claudo Tebaldi, and Attilio L. Stella, "Branching processes and the evolution at the ends of a food
chain,"
Phys. Rev. Lett. 76, 4983 (1996).
- J. J.
Alonso and H. J. Herrman, "Shape of the tail of a two-dimensional sandpile," Phys. Rev. Lett. 76, 4911 (1996).
The authors discuss the simulation of a cellular automaton that
includes gravity, dissipation, and surface roughness.
- M. P. Nightingale and H. W. J. Blote, "Dynamic exponent of the two-dimensional Ising model and Monte
Carlo computation of the subdominant eigenvalue of the stochastic
matrix," Phys. Rev. Lett.
76, 4548 (1996). The authors determine that z = 2.1665.
- M. G. Rozman, M. Urbakh, and J. Klafter, "Stick-Slip Motion and Force
Fluctuations in a driven Two-Wave Potential," Phys. Rev. Lett. 77,
683 (1996).
- Amos Maritan and Jayanth R. Banavar, "Chaos, Noise, and
Synchronization," Phys. Rev. Lett. 72, 1451 (1994).
- I. Goldhirsch
and G. Zanetti, "Clustering instability in dissipative gases," Phys. Rev. Lett. 70, 1619 (1993).
- Zeev Olami, Hans Jacob S. Feder, and Kim Christensen, "Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes," Phys. Rev. Lett. 68, (1992).
Journal of Chemical Physics
- Samantha Weerasinghe and Francois G. Amar, "Absolute classical densities of states for very anharmonic
systems and applications to the evaporation of rare gas clusters,"
J. Chem. Phys. 98,
4967-4983 (1993). The authors use the Nose prescription for constant
temperature dynamics and a multiple histogram method to obtain the
density of states for small clusters.
- Richard E. Gillilan and
Kent R. Wilson, "Shadowing, rare events, and rubber bands. A variational
Verlet algorithm for molecular dynamics," J. Chem. Phys. 97, 1757-1772 (1992). An
interesting use of Hamiltonian's variational principle is discussed.
European Journal of Physics
- Agustin
Gonzalez-Villanueva, H. Nunez-Yepez, and A. L. Salas-Brito, "In velocity space the Kepler orbits are circular," Eur. J.
Phys. 17, 168-171 (1996).
- Peter
Enders, "Huygen's principle and the modelling of propagation," Eur. J. Phys. 17, 226 (1996). A thought provoking
paper.
- Wei-Hsi Liao, "Rectangular mesh renewal numerical method for solving
two-dimensional boundary value problems," Eur. J. Phys.
17 176-179 (1996).
- Daniel Fernandez Hevia and Antonio F. Ranada, "Chaos in the
three-body problem: the Sitnikov case," Eur. J. Phys. 17, 295
(1996). Two stars of equal mass move in Keplerian ellipses in the xy
plane while a test body of negligible mass moves along the z axis.
- Thomas Rage, Vidar
Frette, Geri Wagner, Thomas Walmann, Kim Christensen, and Tao Sun, "Construction of a DLA cluster model,"
Eur. J. Phys. 17, 110-115 (1996). Happy Birthday Paul Meakin!
Physica
- G. J.
Rogers and M. K. Hassan, "Stable distributions in fragmentation processes," Physica A 233, 19-30 (1996). The
authors consider three types of fragmentation processes. For example,
in model A the largest fragment is split into two pieces at every
time step according to some probability distribution. Most of the
work is analytical, but the results are compared to simulations.
- Karoly F. Pal, "The ground state of the cubic spin glass with short-range interactions of Gaussian distribution," Physica A 233, 60-66 (1996). A genetic algorithm and local optimization is used. Earlier work applied the same method to the +-J model.
- Surajit Sen and Somnath Pal, "Metastability and instability in model grain piles: scaling below and at the threshold," Physica A 233, 77-84 (1996). A molecular dynamics method is used for 1196 grains. Energy is absorbed by the side walls.
- Andres R. R. Papa and Constantino Tsallis, "A local-field-type model for immunological systems: time evolution in real and shape spaces," Physica A 233, 85-101 (1996). A model for the interaction of immunological cells that includes their local in real space is developed. Monte Carlo simulations are performed.
- xxx, "A Monte Carlo simulation of the Bernoulli principle," Physica
A 233, 153-162 (1996). A Monte Carlo simulation of the
effusion of an ideal gas thru a small orifice is considered. A prior
understanding of the Euler equation is desirable.
- M. Argollo de Menezes, A. Racco, and
T. J. P. Penna, "Why trees live longer," Physica A 233, 221-225 (1996). The authors use
a bit string model for biological aging similar to that discussed by
D. Stauffer in Computers in Physics 10, 341 (1996).
- Dirk Helbing, "Derivation and empirical validation of a refined traffic flow
model," Physica A 233, 253-282 (1996). Good
background for discussion of kinetic equation approach.
- F. L. Roman, J. A. White, and S. Velasco, "Probability distribution function for the random sequential
adsorption of hard disks,"
Physica A 233, 283-292 (1996). The fluctuations in the number
of disks in a finite subvolume are considered.
- Constantino Tsallis and
Daniel A. Stariolo, "Generalized simulated annealing," Physica A 233, 395-406 (1996). An
excellent discussion of simulated annealing methods. An excellent
basis for a student project.
- D. Stauffer,
P. M. C. de Oliveira, S. Moss de Oliveira, R. M. Zorzenon dos Santos, "Monte Carlo simulations of sexual reproduction,"
Physica A 231, 504 (1996). This article is a good follow-up to
Dietrich's Stauffer's computer simulation column, "Getting Older -
Monte Carlo Simulations of Biological Aging," Computers in Physics
10(4), 341 (1996).
- S. J.
Feingold, "Monte Carlo simulation of Alaska wolf survival," Physica A 231, 499 (1996). Authors uses the Penna
bit-string model.
- Luis A. Nunes Amaral
and Kent Baekgaard Lauritsen, "Energy avalanches in a rice-pile model," Physica A 231, 608 (1996). A
simple one-dimensional model of self-organized criticality and
friction.
- L.
Benguigui, "A new aggregation model: application to town growth," Physica A 219, 13-26 (1995). A variation of the
Eden model is discussed in which a site is occupied only after it is
visited p times. The difference is that a site is added to the list
of perimeter sites immediately after the first visit (and
independently of whether it is occupied). The computed results for
the local density N(r) are compared with data for N(r) for the cities
of Baltimore, Paris and London. Related articles are Ivars Peterson, "The shapes of
cities: Mapping out fractal models of urban growth,"
Science News 149, 8 (1996). Peterson sites the following
additional references: Batty and Paul Longley, "Fractal Cities: A
Geometry of Form and Function," Academic Press (1994) and Hernan A.
Makse, H. Eugene Stanley, and Shlomo Havlin, Nature, Oct. 19, 1995.
- Kai Nagel and Hans J.
Herrmann, "Deterministic models for traffic jams," Physica A 199, 254 (1993).
J. Physics A: Math. Gen.
- C. Godreche, J. P. Bouchaud, and M. Mezard, "Entropy barriers and slow relaxation in some random walk
models," J. Phys. A
28, L603-L611 (1995). Consider N distinguishable particles
distributed at t = 0 among M boxes. Model A. At each time step, a
particle is chosen at random and put in one of the non-empty boxes
chosen at random. Model B. The particles are now considered to be
indistinguishable. At each time step, a non-empty box is chosen at
random. A particle is withdrawn from this box and put into one of the
other non-empty boxes chosen at random. Model C. The particles are
distinguishable. At each time step, two particles are chosen at
random. One of the particles is put into the box to which the second
one belongs. In each case determine A(t)/N, where A(t) is the number
of non-empty (active) boxes. In which model is equilibrium
established more quickly? What is the distribution of filled boxes?
Other journals
- Boquan Li,
Jing Wang, Bing Wang, Wenhan Liu, and Ziqin Wu, "Computer simulations of bacterial-colony formation," Europhysics Letts.
30, 239 (1995).
- Brian Hayes, "The way the ball bounces," Amer. Sci. 84,
331 (1996). An excellent discussion of molecular dynamics and
associated cellular automata.
- Hideo Kaburaki and Masahiko Machida, "Thermal conductivity in one-dimensional lattices of
Fermi-Pasta-Ulam type," Phys.
Letts. A 181, 85-90 (1993). The thermal conductivity is
computed by coupling the ends of the lattice to a heat bath.
Electronic preprints
- Kai Nagel, Paula Stretz,
Martin Pieck, Rick Donnelly, Christopher L. Barrett, "TRANSIMS traffic flow characteristics,"
adap-org/9710003.
- Rama Cont and Jean-Phillippe Bouchaud, "Herd behavior and aggregate fluctuations in financial
markets," cond-mat/9712318.
- Bambi Hu, Baowen
Li, and Hong Zhao, "Heat conduction in one-dimensional chains," Phys. Rev. E 57, 2992 (1998),
cond-mat/9712064.
- Sang-Yoon Kim, "Nonlinear Dynamics of a Damped Magnetic Oscillator," download
Please contribute your suggestions and ideas. Send them to Harvey Gould, hgould@guessu.edu.
Updated 31 January 2000.