In this paper, we introduce a graphic processing unit (GPU)-based framework for simulating particle trajectories under both static and dynamic force fields. By exploiting the highly parallel nature of the problem and making efficient use of the available hardware, our simulator exhibits a significant speedup over its CPU-based analog. We apply our framework to a specific experimental simulation: the computation of trapping probabilities associated with micron-sized silica beads in optical trapping workbenches. When evaluating large numbers of trajectories (4096), we see approximately a 356 times speedup of the GPU-based simulator over its CPU-based counterpart.

References

References
1.
Tolle
,
D.
, and
Le Novere
,
N.
, 2010, “
Brownian Ddiffusion of AMPA Receptors is Sufficient to Explain Fast Onset of LTP
,”
BMC Syst. Biol.
,
4
(
1
), p.
25
.
2.
Broadie
,
M.
, and
Kaya
,
O.
, 2006, “
Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes
,”
Oper. Res.
,
54
(
2
), pp.
217
231
.
3.
Bhushan
,
B.
, ed., 2004,
Springer Handbook of Nanotechnology
,
Springer-Verlag
,
New York, NY
.
4.
Ratner
,
M.
, and
Ratner
,
D.
, 2002,
Nanotechnology: A Gentle Introduction to the Next Big Idea
,
Prentice-Hall
,
Upper Saddle River, NJ
.
5.
Niemeyer
,
C.
, and
Mirkin
,
C. A.
, eds., 2004,
Nanobiotechnology: Concepts, Applications and Perspectives
,
Wiley-VCH
,
Germany
.
6.
Wilson
,
M.
,
Kannangara
,
K.
,
Smith
,
G.
,
Simmons
,
M.
, and
Raquse
,
B.
, 2002.
Nanotechnology: Basic Science and Emerging Technologies
.
Chapman and Hall/CRC
,
Boca Raton, FL
.
7.
Requicha
,
A.
, and
Arbuckle
,
D.
, 2006, “
CAD/CAM for Nanoscale Self-Assembly
,”
IEEE Comput. Graph. Appl.
,
26
(
2
), pp.
88
91
.
8.
Peng
,
T.
,
Balijepalli
,
A.
,
Gupta
,
S.
, and
LeBrun
,
T.
, 2009. “
Algorithms for Extraction of Nanowire Lengths and Positions From Optical Section Microscopy Image Sequence
,”
J. Comput. Inf. Sci. Eng.
,
9
, p.
041007
.
9.
Banerjee
,
A.
,
Pomerance
,
A.
,
Losert
,
W.
, and
Gupta
,
S.
, 2010, “
Developing a Stochastic Dynamic Programming Framework for Optical Tweezer-Based Automated Particle Transport Operations
,”
IEEE Trans. Autom. Sci. Eng.
,
7
(
2
), pp.
218
227
.
10.
Ashkin
,
A.
, 1970, “
Acceleration and Trapping of Particles by Radiation Pressure
,”
Phys. Rev. Lett.
,
24
(
4
), pp.
156
159
.
11.
Ashkin
,
A.
,
Dziedzic
,
J.
,
Bjorkholm
,
J.
, and
Chu
,
S.
, 1986, “
Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles
,”
Opt. Lett.
,
11
(
5
), p.
288
.
12.
Banerjee
,
A.
,
Balijepalli
,
A.
,
Gupta
,
S.
, and
LeBrun
,
T.
, 2009, “
Generating Simplified Trapping Probability Models From Simulation of Optical Tweezers System
,”
J. Comput. Inf. Sci. Eng.
,
9
, p.
021003
.
13.
Balijepalli
,
A.
,
LeBrun
,
T.
, and
Gupta
,
S.
, 2010, “
Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance
,”
J. Comput. Inf. Sci. Eng.
,
10
, p.
011010
.
14.
Owens
,
J. D.
,
Luebke
,
D.
,
Govindaraju
,
N.
,
Harris
,
M.
,
Krüger
,
J.
,
Lefohn
,
A. E.
, and
Purcell
,
T.
, 2007, “
A survey of general-purpose computation on graphics hardware
,”
Comput. Graph. Forum
,
26
(
1
), pp.
80
113
.
15.
James
,
G.
, 2001, “
Operations for Hardware-Accelerated Procedural Texture Animation
,”
Game Programming Gems 2
,
Mark
DeLoura
, ed.,
Charles River Media
, pp.
497
509
.
16.
Li
,
W.
,
Wei
,
X.
, and
Kaufman
,
A. E.
, 2003, “
Implementing Lattice Boltzmann Computation on Graphics Hardware
,”
Visual Comput.
,
19
(
7–8
), pp.
444
456
.
17.
Wei
,
X.
,
Zhao
,
Y.
,
Fan
,
Z.
,
Li
,
W.
,
Qiu
,
F.
,
Yoakum-Stover
,
S.
, and
Kaufman
,
A. E.
, 2004, “
Lattice-Based Flow Field Modeling
,”
IEEE Trans. Vis. Comput. Graph.
,
10
(
6
), pp.
719
729
.
18.
Harris
,
M.
, 2005, “
Fast Fluid Dynamics Simulation on the GPU
,” in SIGGRAPH ’05: ACM SIGGRAPH 2005 Courses,
ACM
, p.
220
.
19.
Hagen
,
T. R.
,
Lie
,
K.-A.
, and
Natvig
,
J. R.
, 2006, “
Solving the Euler Equations on Graphics Processing Units
,”
International Conference on Computational Science
, Vol.
3994
(
2
) pp.
220
227
, http://www.mendeley.com/research/solving-euler-equations-graphics-processing-units-5/.
20.
Bolz
,
J.
,
Farmer
,
I.
,
Grinspun
,
E.
, and
Schröoder
,
P.
, 2003, “
Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid
,”
in SIGGRAPH ’03: ACM SIGGRAPH 2003 Papers
,
ACM
, pp.
917
924
.
21.
Krüger
,
J.
, and
Westermann
,
R.
, 2003, “
Linear Algebra Operators for GPU Implementation of Numerical Algorithms
,”
ACM Trans. Graphics
,
22
(
3
), pp.
908
916
.
22.
Liu
,
Y.
,
Liu
,
X.
, and
Wu
,
E.
, 2004, “
Real-Time 3D Fluid Simulation on GPU With Complex Obstacles
,”
in Pacific Conference on Computer Graphics and Applications
,
IEEE Computer Society
, pp.
247
256
.
23.
Sander
,
P.
,
Tatarchuk
,
N.
, and
Mitchell
,
J. L.
, 2006, “
Explicit Early-Z Culling for Efficient Fluid Flow Simulation
,”
ShaderX5: Advanced Rendering Techniques
,
Engel
Wolfgang
, ed.,
Charles River Media
,
Cambridge, MA
, pp.
553
564
.
24.
Heidrich
,
W.
,
Westermann
,
R.
,
Seidel
,
H.-P.
, and
Ertl
,
T.
, 1999, “
Applications of Pixel Textures in Visualization and Realistic Image Synthesis
,”
I3D ’99: Proceedings of the 1999 Symposium on Interactive 3D Graphics
,
ACM
, pp.
127
134
.
25.
Jobard
,
B.
,
Erlebacher
,
G.
, and
Hussaini
,
M. Y.
, 2001, “
Lagrangian-Eulerian Advection for Unsteady Flow Visualization
,”
Proceedings of the Conference on Visualization 2001 (VIS-01)
,
T.
Ertl
,
K.
Joy
, and
A.
Varshney
, eds.,
IEEE Computer Society
, pp.
53
60
.
26.
Weiskopf
,
D.
,
Hopf
,
M.
, and
Ertl
,
T.
, 2001, “
Hardware-Accelerated Visualization of Time-Varying 2-D and 3-D Vector Fields by Texture Advection Via Programmable Per-Pixel Operations
,”
Vision, Modeling, and Visualization
, pp.
439
446
.
27.
Juba
,
D.
, and
Varshney
,
A.
, 2008, “
Parallel Stochastic Measurement of Molecular Surface Area
,”
J. Mol. Graphics Modell.
,
27
(
1
), pp.
82
87
.
28.
Reicherter
,
M.
,
Haist
,
T.
,
Zwick
,
S.
,
Burla
,
A.
,
Seifert
,
L.
, and
Osten
,
W.
, 2005, “
Fast Hologram Computation and Aberration Control for Holographic Tweezers
,”
Optical Trapping and Optical Micromanipulation II
,
K.
Dholakia
and
G. C.
Spalding
, eds., Vol.
5930
(1),
SPIE
,
San Diego, CA, USA
, http://link.aip.org/link/?PSI/5930/59301Y/1http://link.aip.org/link/?PSI/5930/59301Y/1, p.
59301Y
.
29.
Haist
,
T.
,
Reicherter
,
M.
,
Wu
,
M.
, and
Seifert
,
L.
, 2006, “
Using Graphics Boards to Compute Holograms
,”
Comput. Sci. Eng.
,
8
(
1
), pp.
8
13
.
30.
Hermerschmidt
,
A.
,
Kruger
,
S.
,
Haist
,
T.
,
Zwick
,
S.
,
Warber
,
M.
, and
Osten
,
W.
, 2007, “
Holographic Optical Tweezers With Real-Time Hologram Calculation Using a Phase-Only Modulating LCOS-Based SL at 1064 nm
,”
Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series
, Vol.
6905
, p.
7
.
31.
Wright
,
W.
,
Sonek
,
G.
, and
Berns
,
M.
, 1994, “
Parametric Study of the Forces on Microspheres Held by Optical Tweezers
,”
Appl. Opt.
,
33
(
9
), pp.
1735
1748
.
32.
Gardiner
,
C.
, 1985,
Handbook of Stochastic Methods
,
Springer
,
Berlin
.
33.
Langevin
,
P.
, 1908, “
On the Theory of Brownian Motion
,”
C. R. Acad. Sci.
,
146
, pp.
530
533
.
34.
Girault
,
V.
, and
Raviart
,
P.
, 1979, “
Finite Element Approximation of the Navier-Stokes Equations
,”
Lecture Notes in Mathematics
,
Springer–Verlag
,
Berlin
, p.
749
.
35.
Weissbluth
,
M.
, 1989,
Photon-Atom Interactions
,
Academic Press
,
San Diego, CA
.
36.
Grassia
,
P.
, 2001, “
Dissipation, Fluctuations, and Conservation Laws
,”
Am. J. Phys.
,
69
, p.
113
.
37.
Jameson
,
A.
,
Schmidt
,
W.
, and
Turkel
,
E.
, 1981, “
Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Ttime-Stepping Schemes
,”
AIAA Pap.
,
1259
, p.
1981
.
38.
Allen
,
M.
, and
Tildesley
,
D.
, 1990,
Computer Simulation of Liquids
,
Oxford University Press
,
USA
.
39.
Verlet
,
L.
, 1968, “
Computer Experiments on Classical Fluids. II. Equilibrium Correlation Functions
,”
Phys. Rev
,
165
(
1
), pp.
201
14
.
40.
van Meel
,
J.
,
Arnold
,
A.
,
Frenkel
,
D.
,
Zwart
,
S. P.
, and
Belleman
,
R.
, 2008, “
Harvesting Graphics Power for MD Simulations
,”
Mol. Simul.
,
34
, pp.
259
266
.
41.
Hines
,
W. W.
,
Montgomery
,
D. C.
,
Goldsman
,
D. M.
, and
Borror
,
C. M.
, 2003,
Probability and Statistics in Engineering
,
4 ed.
,
Wiley
,
New York
.
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