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

  1. F. Cecconi, R. Livi, and A. Politti, "Fuzzy transition region in a one-dimensional coupled-stable-map lattice," Phys. Rev. E 57, 2703 (1998).

  2. Jean-Pierre Goedgebuer, Laurent Larger, and Henri Porte, "Chaos in wavelength with a feedback tunable laser diode," Phys. Rev. E 57, 2795 (1998).

  3. 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).

  4. 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).

  5. 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.

  6. 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.

  7. Zbigniew Koza and Haim Taitelbaum, "Reaction-diffusion front in a system with strong quenched disorder," Phys. Rev. E 56, 6387 (1997). keyword: Sinai disorder.
  8. T. T. Rautiainen, M. J. Alava, and K. Kaski, "Dynamics of fracture in dissipative systems," Phys. Rev. E 56, (1997). keyword: crack.

  9. 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.

  10. Ezequiel V. Albano, "Properties of the interface generated by the collision of two growing interfaces," Phys. Rev. E 56, 7301 (1997).

  11. Claus Wilke and Thomas Martinetz, "Simple model of evolution with variable system size," Phys. Rev. E 56, 7128 (1997).

  12. 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).

  13. 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.

  14. 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.

  15. 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.

  16. A. Malthe-Sorenssen, "Kinetic grain model for sandpiles," Phys. Rev. E 54, 2261 (1996). Another sandpile model.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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?

  24. Kai Nagel, "Particle hopping models and traffic flow theory," Phys. Rev. E 53, 4655 (1996).

  25. 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.

  26. 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.

  27. 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).

  28. 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.

  29. 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.

  30. 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.

  31. 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.

  32. 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.

  33. 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.

  34. 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.

  35. 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.

  36. 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.

  37. 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.

  38. 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.

  39. 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.

  40. 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.

  41. 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.

  42. 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.

  43. 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.

  44. 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.

  45. George G. Szpiro, "Forecasting chaotic time series with genetic algorithms," Phys. Rev. E 55, 2557 (1997).

  46. Toru Ohira and Ryusuke Sawatari, "Delay estimation from noisy time series," Phys. Rev. E 55, R2077 (1997).

Physical Review Letters

  1. Rolando Castro and Tim Sauer, "Chaotic Stochastic Resonance: Noise-Enhanced reconstruction of Attractors," Phys. Rev. Lett. 79, 1030 (1997).

  2. Surajit Sen, Robert S. Sinkovits, and Soumya Chakravarti, "Algebraic Relaxation Laws for Classical Particles in 1D Anharmonic Potentials," Phys. Rev. Lett. 77, 4855 (1996).

  3. 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.

  4. 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).

  5. 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.

  6. 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.

  7. 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).

  8. Amos Maritan and Jayanth R. Banavar, "Chaos, Noise, and Synchronization," Phys. Rev. Lett. 72, 1451 (1994).

  9. I. Goldhirsch and G. Zanetti, "Clustering instability in dissipative gases," Phys. Rev. Lett. 70, 1619 (1993).

  10. 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

  1. 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.

  2. 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

  1. 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).

  2. Peter Enders, "Huygen's principle and the modelling of propagation," Eur. J. Phys. 17, 226 (1996). A thought provoking paper.

  3. Wei-Hsi Liao, "Rectangular mesh renewal numerical method for solving two-dimensional boundary value problems," Eur. J. Phys. 17 176-179 (1996).

  4. 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.

  5. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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).

  7. 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.

  8. 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.

  9. 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.

  10. 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).

  11. S. J. Feingold, "Monte Carlo simulation of Alaska wolf survival," Physica A 231, 499 (1996). Authors uses the Penna bit-string model.

  12. 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.

  13. 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.

  14. Kai Nagel and Hans J. Herrmann, "Deterministic models for traffic jams," Physica A 199, 254 (1993).

J. Physics A: Math. Gen.

  1. 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

  1. Boquan Li, Jing Wang, Bing Wang, Wenhan Liu, and Ziqin Wu, "Computer simulations of bacterial-colony formation," Europhysics Letts. 30, 239 (1995).

  2. Brian Hayes, "The way the ball bounces," Amer. Sci. 84, 331 (1996). An excellent discussion of molecular dynamics and associated cellular automata.

  3. 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

  1. Kai Nagel, Paula Stretz, Martin Pieck, Rick Donnelly, Christopher L. Barrett, "TRANSIMS traffic flow characteristics," adap-org/9710003.

  2. Rama Cont and Jean-Phillippe Bouchaud, "Herd behavior and aggregate fluctuations in financial markets," cond-mat/9712318.

  3. Bambi Hu, Baowen Li, and Hong Zhao, "Heat conduction in one-dimensional chains," Phys. Rev. E 57, 2992 (1998), cond-mat/9712064.

  4. 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.