Publications
Books
Modeling MEMS and NEMS CRC Press, Baton Rouge, 2002
Papers
B. Aksoylu, D. Bernstein, S. Bond, and M. Holst, Generating Initial Data in General Relativity using Adaptive Finite Element Methods, arXiv:0801.3142. Submitted January 2008, last revised April 2009.
D. Bernstein, Optimal Prediction of Burgers’s Equation, Multiscale Modeling and Simulation, 6, 27-52 (2007).
D. Bernstein, Simulating Mesoscopic Reaction-Diffusion Systems using the Gillespie Algorithm, Physical Review E 71, 041103 (2005).
K. Jones and D. Bernstein, The Self-Gravitating Bose-Einstein Condensate, Classical and Quantum Gravity, 18, 1513-1533 (2001).
D. Bernstein, E. Giladi, and K. Jones, Eigenstates of the Gravitational Schrodinger Equation, Modern Physics Letters A, 13, 2327-2336 (1998).
P. Anninos, D. Bernstein, S. Brandt, D. Hobill, E. Seidel, and L. Smarr, Oscillating Apparent Horizons in Numerically Generated Spacetimes, Australian Journal of Physics, 48, 1027-1043 (1995).
P. Anninos, D. Bernstein, S. Brandt, J. Libson, J. Masso, E. Seidel, L. Smarr, W-M. Suen, and P. Walker, Dynamics of Apparent and Event Horizons, Physical Review Letters, 74, 630-633 (1995).
D. Bernstein, D. Hobill, E. Seidel, L. Smarr, and J. Towns Numerically Generated Axisymmetric Black Hole Spacetimes–Numerical Methods and Code Tests, Physical Review D50, 5000-5024 (1994).
D. Bernstein, D. Hobill, E. Seidel, and L. Smarr, Initial Data for the Black Hole Plus Brill Wave Spacetime, Physical Review D50, 3760-3782 (1994).
D. Bernstein and K.P. Tod, Penrose’s Quasi-local Mass in a Numerically Computed Spacetime, Physical Review D49, 2808-2819 (1994).
P. Anninos, M. Bajuk, D. Bernstein, E. Seidel, and L. Smarr Visualizing Black Hole Spacetimes, IEEE Computer Graphics and Applications, 13, 12-14, January 1993.
A. Abrahams, D. Bernstein, D. Hobill, E. Seidel, and L. Smarr, Numerically Generated Black Hole Spacetimes–Interaction with Gravitational Waves, Physical Review, D45, 3544-3558 (1992).
Conference Proceedings
J. Pelesko, D. Bernstein, and J. McCuan, Symmetry and Symmetry Breaking in Electrostatic MEMS, Proceedings of the Sixth International Conference on Modeling and Simulation of Microsystems, 304-307, San Francisco, February 2003.
P. Guidotti and D. Bernstein, Modeling and Analysis of Hysteresis Phenomena in Electrostatic Zipper Actuators, Proceedings of the Fourth International Conference on Modeling and Simulation of Microsystems, 306-309, Hilton Head, March 2001.
D. Bernstein, J. Pelesko, and P. Guidotti, Mathematical Analysis of Electrostatically Actuated MEMS Devices, Proceedings of the Third International Conference on Modeling and Simulation of Microsystems, 489-492, San Diego, March 2000.
H.J. Lee, S.B. Crary, B. Affour, D. Bernstein, Y.B. Gianchandani, D.M. Woodcock, and M.A. Maher, Generation of a Metamodel for a Micromachined Accelerometer using T-Spice and the I_z-Optimality Option of I-OPT, Proceedings of the Third International Conference on Modeling and Simulation of Microsystems, 201-204, San Diego, March 2000.
B. Dyne and D. Bernstein, A Correct-By-Construction Approach to MEMS Design and Analysis, Proceedings of SPIE, 142-149, Paris, March 1999.
J. Gong, S. Wedge, and D. Bernstein, Mesh Refinement for Hybrid FEM in the Analysis of Printed Circuit Antennas, Proceedings of the 4th Annual Review of Progress in Applied Computational Electromagnetics, 2, 750-755, 1998.
D. Bernstein and M. Holst, A 3D Finite Element Solver for the Initial Value Problem, Proceedings of the Eighteenth Texas Symposium on Relativistic Astrophysics, 610-612, Chicago, December 1996.
D. Bernstein, D. Hobill, David, E. Seidel, L. Smarr, and J. Towns, Gravitational waves from dynamic black hole spacetimes, Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, 312-316, Waterloo, 1993.
H. Fritzsche, J. Kakalios, and D. Bernstein, Search for Reversible Light-Induced Changes in the Si-H Absorption Bands of a-Si:H, Optical Effects in Amorphous Semiconductors, Snowbird, August 1984.
Patents
E. Quevy, D. Bernstein, M. Motiee, Out-of-plane MEMS resonator with static out-of-plane deflection, Silicon Laboratories, January 2014, US 8629739 B2.
E. Quevy, D. Bernstein, M. Motiee, Out-of-plane MEMS resonator with static out-of-plane deflection, Silicon Laboratories, September 2012, US 8258893.
E. Quevy, D. Bernstein, M. Motiee, Out-of-plane MEMS resonator with static out-of-plane deflection, Silicon Laboratories, August 2011, US 7999635.
D. Bernstein, MEMS structure have a stress-inducer temperature-compensated resonator member, Silicon Laboratories, May 2011, US 7944124.
E. Quevy, D. Bernstein, Method for temperature compensation in MEMS resonators with isolated regions of distinct material, Silicon Clocks, December 2009, US 7639104.
D. Bernstein, R. Howe, E. Quevy, MEMS structure have a compensated resonating member, Silicon Clocks, September 2009, US 7591201.
R. Howe, E. Quevy, D. Bernstein, MEMS structure having a stress inverter temperature-compensating resonating member, Silicon Clocks, April 2009, US 7514853.