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+  uri = {<Go to ISI>://A1991EU81400029},
-+
+@ARTICLE{Andersen1983,
-+
+  author = {H. C. Andersen},
-+
+  title = {Rattle - a Velocity Version of the Shake Algorithm for Molecular-Dynamics
-+
+        Calculations},
-+
+  journal = {Journal of Computational Physics},
-+
+  year = {1983},
-+
+  volume = {52},
-+
+  pages = {24-34},
-+
+  number = {1},
-+
+  annote = {Rq238 Times Cited:559 Cited References Count:14},
-+
+  issn = {0021-9991},
-+
+  uri = {<Go to ISI>://A1983RQ23800002},
-+
+}
-+
+@ARTICLE{Auerbach2005,
+  author = {A. Auerbach},
+  title = {Gating of acetylcholine receptor channels: Brownian motion across
+  uri = {<Go to ISI>://000221146400009},
-+
+@ARTICLE{Barojas1973,
-+
+  author = {J. Barojas and D. Levesque},
-+
+  title = {Simulation of Diatomic Homonuclear Liquids},
-+
+  journal = {Phys. Rev. A},
-+
+  year = {1973},
-+
+  volume = {7},
-+
+  pages = {1092-1105},
-+
+}
-+
+@ARTICLE{Barth1998,
+  author = {E. Barth and T. Schlick},
+  title = {Overcoming stability limitations in biomolecular dynamics. I. Combining
+@ARTICLE{Berkov2005,
+  author = {D. V. Berkov and N. L. Gorn},
-–
+  title = {Stochastic dynamic simulations of fast remagnetization processes:
-–
+        recent advances and applications},
-–
+  journal = {Journal of Magnetism and Magnetic Materials},
-–
+  year = {2005},
-–
+  volume = {290},
-–
+  pages = {442-448},
-–
+  month = {Apr},
-–
+  abstract = {Numerical simulations of fast remagnetization processes using stochastic
-–
+        dynamics are widely used to study various magnetic systems. In this
-–
+        paper, we first address several crucial methodological problems
-–
+        of such simulations: (i) the influence of finite-element discretization
-–
+        on simulated dynamics, (ii) choice between Ito and Stratonovich
-–
+        stochastic calculi by the solution of micromagnetic stochastic equations
-–
+        of motion and (iii) non-trivial correlation properties of the random
-–
+        (thermal) field. Next, we discuss several examples to demonstrate
-–
+        the great potential of the Langevin dynamics for studying fast remagnetization
-–
+        processes in technically relevant applications: we present numerical
-–
+        analysis of equilibrium magnon spectra in patterned structures,
-–
+        study thermal noise effects on the magnetization dynamics of nanoelements
-–
+        in pulsed fields and show some results for a remagnetization dynamics
-–
+        induced by a spin-polarized current. (c) 2004 Elsevier B.V. All
-–
+        rights reserved.},
-–
+  annote = {Part 1 Sp. Iss. SI 922KU Times Cited:2 Cited References Count:25},
-–
+  issn = {0304-8853},
-–
+  uri = {<Go to ISI>://000228837600109},
-–
+}
-–
-–
+@ARTICLE{Berkov2005a,
-–
+  author = {D. V. Berkov and N. L. Gorn},
+  title = {Magnetization precession due to a spin-polarized current in a thin
+        nanoelement: Numerical simulation study},
+  journal = {Physical Review B},
+  uri = {<Go to ISI>://000232228500058},
-+
+@ARTICLE{Berkov2005a,
-+
+  author = {D. V. Berkov and N. L. Gorn},
-+
+  title = {Stochastic dynamic simulations of fast remagnetization processes:
-+
+        recent advances and applications},
-+
+  journal = {Journal of Magnetism and Magnetic Materials},
-+
+  year = {2005},
-+
+  volume = {290},
-+
+  pages = {442-448},
-+
+  month = {Apr},
-+
+  abstract = {Numerical simulations of fast remagnetization processes using stochastic
-+
+        dynamics are widely used to study various magnetic systems. In this
-+
+        paper, we first address several crucial methodological problems
-+
+        of such simulations: (i) the influence of finite-element discretization
-+
+        on simulated dynamics, (ii) choice between Ito and Stratonovich
-+
+        stochastic calculi by the solution of micromagnetic stochastic equations
-+
+        of motion and (iii) non-trivial correlation properties of the random
-+
+        (thermal) field. Next, we discuss several examples to demonstrate
-+
+        the great potential of the Langevin dynamics for studying fast remagnetization
-+
+        processes in technically relevant applications: we present numerical
-+
+        analysis of equilibrium magnon spectra in patterned structures,
-+
+        study thermal noise effects on the magnetization dynamics of nanoelements
-+
+        in pulsed fields and show some results for a remagnetization dynamics
-+
+        induced by a spin-polarized current. (c) 2004 Elsevier B.V. All
-+
+        rights reserved.},
-+
+  annote = {Part 1 Sp. Iss. SI 922KU Times Cited:2 Cited References Count:25},
-+
+  issn = {0304-8853},
-+
+  uri = {<Go to ISI>://000228837600109},
-+
+}
-+
+@ARTICLE{Berkov2002,
+  author = {D. V. Berkov and N. L. Gorn and P. Gornert},
+  title = {Magnetization dynamics in nanoparticle systems: Numerical simulation
+  annote = {Sm173 Times Cited:143 Cited References Count:22},
+  issn = {0009-2614},
+  uri = {<Go to ISI>://A1984SM17300007},
-+
+}
-+
-+
+@ARTICLE{Budd1999,
-+
+  author = {C. J. Budd and G. J. Collins and W. Z. Huang and R. D. Russell},
-+
+  title = {Self-similar numerical solutions of the porous-medium equation using
-+
+        moving mesh methods},
-+
+  journal = {Philosophical Transactions of the Royal Society of London Series
-+
+        a-Mathematical Physical and Engineering Sciences},
-+
+  year = {1999},
-+
+  volume = {357},
-+
+  pages = {1047-1077},
-+
+  number = {1754},
-+
+  month = {Apr 15},
-+
+  abstract = {This paper examines a synthesis of adaptive mesh methods with the
-+
+        use of symmetry to study a partial differential equation. In particular,
-+
+        it considers methods which admit discrete self-similar solutions,
-+
+        examining the convergence of these to the true self-similar solution
-+
+        as well as their stability. Special attention is given to the nonlinear
-+
+        diffusion equation describing flow in a porous medium.},
-+
+  annote = {199EE Times Cited:4 Cited References Count:14},
-+
+  issn = {1364-503X},
-+
+  uri = {<Go to ISI>://000080466800005},
+@ARTICLE{Camp1999,
+  annote = {221EN Times Cited:14 Cited References Count:66},
+  issn = {0021-9606},
+  uri = {<Go to ISI>://000081711200038},
-+
+}
-+
-+
+@ARTICLE{Channell1990,
-+
+  author = {P. J. Channell and C. Scovel},
-+
+  title = {Symplectic Integration of Hamiltonian-Systems},
-+
+  journal = {Nonlinearity},
-+
+  year = {1990},
-+
+  volume = {3},
-+
+  pages = {231-259},
-+
+  number = {2},
-+
+  month = {may},
-+
+  annote = {Dk631 Times Cited:152 Cited References Count:34},
-+
+  issn = {0951-7715},
-+
+  uri = {<Go to ISI>://A1990DK63100001},
-+
+}
-+
-+
+@ARTICLE{Chen2003,
-+
+  author = {B. Chen and F. Solis},
-+
+  title = {Explicit mixed finite order Runge-Kutta methods},
-+
+  journal = {Applied Numerical Mathematics},
-+
+  year = {2003},
-+
+  volume = {44},
-+
+  pages = {21-30},
-+
+  number = {1-2},
-+
+  month = {Jan},
-+
+  abstract = {We investigate the asymptotic behavior of systems of nonlinear differential
-+
+        equations and introduce a family of mixed methods from combinations
-+
+        of explicit Runge-Kutta methods. These methods have better stability
-+
+        behavior than traditional Runge-Kutta methods and generally extend
-+
+        the range of validity of the calculated solutions. These methods
-+
+        also give a way of determining if the numerical solutions are real
-+
+        or spurious. Emphasis is put on examples coming from mathematical
-+
+        models in ecology. (C) 2002 IMACS. Published by Elsevier Science
-+
+        B.V. All rights reserved.},
-+
+  annote = {633ZD Times Cited:0 Cited References Count:9},
-+
+  issn = {0168-9274},
-+
+  uri = {<Go to ISI>://000180314200002},
+@ARTICLE{Cheung2004,
+  annote = {704QL Times Cited:48 Cited References Count:60},
+  issn = {0022-2836},
+  uri = {<Go to ISI>://000184351300022},
-+
+}
-+
-+
+@ARTICLE{Greengard1994,
-+
+  author = {L. Greengard},
-+
+  title = {Fast Algorithms for Classical Physics},
-+
+  journal = {Science},
-+
+  year = {1994},
-+
+  volume = {265},
-+
+  pages = {909-914},
-+
+  number = {5174},
-+
+  month = {Aug 12},
-+
+  abstract = {Some of the recently developed fast summation methods that have arisen
-+
+        in scientific computing are described. These methods require an
-+
+        amount of work proportional to N or N log N to evaluate all pairwise
-+
+        interactions in an ensemble of N particles. Traditional methods,
-+
+        by contrast, require an amount of work proportional to N-2. AS a
-+
+        result, large-scale simulations can be carried out using only modest
-+
+        computer resources. In combination with supercomputers, it is possible
-+
+        to address questions that were previously out of reach. Problems
-+
+        from diffusion, gravitation, and wave propagation are considered.},
-+
+  annote = {Pb499 Times Cited:99 Cited References Count:44},
-+
+  issn = {0036-8075},
-+
+  uri = {<Go to ISI>://A1994PB49900031},
-+
+}
-+
-+
+@ARTICLE{Greengard1987,
-+
+  author = {L. Greengard and V. Rokhlin},
-+
+  title = {A Fast Algorithm for Particle Simulations},
-+
+  journal = {Journal of Computational Physics},
-+
+  year = {1987},
-+
+  volume = {73},
-+
+  pages = {325-348},
-+
+  number = {2},
-+
+  month = {Dec},
-+
+  annote = {L0498 Times Cited:899 Cited References Count:7},
-+
+  issn = {0021-9991},
-+
+  uri = {<Go to ISI>://A1987L049800006},
-+
+@ARTICLE{Hairer1997,
-+
+  author = {E. Hairer and C. Lubich},
-+
+  title = {The life-span of backward error analysis for numerical integrators},
-+
+  journal = {Numerische Mathematik},
-+
+  year = {1997},
-+
+  volume = {76},
-+
+  pages = {441-462},
-+
+  number = {4},
-+
+  month = {Jun},
-+
+  abstract = {Backward error analysis is a useful tool for the study of numerical
-+
+        approximations to ordinary differential equations. The numerical
-+
+        solution is formally interpreted as the exact solution of a perturbed
-+
+        differential equation, given as a formal and usually divergent series
-+
+        in powers of the step size. For a rigorous analysis, this series
-+
+        has to be truncated. In this article we study the influence of this
-+
+        truncation to the difference between the numerical solution and
-+
+        the exact solution of the perturbed differential equation. Results
-+
+        on the long-time behaviour of numerical solutions are obtained in
-+
+        this way. We present applications to the numerical phase portrait
-+
+        near hyperbolic equilibrium points, to asymptotically stable periodic
-+
+        orbits and Hopf bifurcation, and to energy conservation and approximation
-+
+        of invariant tori in Hamiltonian systems.},
-+
+  annote = {Xj488 Times Cited:50 Cited References Count:19},
-+
+  issn = {0029-599X},
-+
+  uri = {<Go to ISI>://A1997XJ48800002},
-+
+}
-+
+@ARTICLE{Hao1993,
+  author = {M. H. Hao and M. R. Pincus and S. Rackovsky and H. A. Scheraga},
+  title = {Unfolding and Refolding of the Native Structure of Bovine Pancreatic
+  uri = {<Go to ISI>://A1992JU25100002},
-+
+@BOOK{Hockney1981,
-+
+  title = {Computer Simulation Using Particles},
-+
+  publisher = {McGraw-Hill},
-+
+  year = {1981},
-+
+  author = {R.W. Hockney and J.W. Eastwood},
-+
+  address = {New York},
-+
+}
-+
+@ARTICLE{Huh2004,
+  author = {Y. Huh and N. M. Cann},
+  title = {Discrimination in isotropic, nematic, and smectic phases of chiral
+  year = {2003},
+  volume = {331},
+  pages = {281-299},
-+
+}
-+
-+
+@ARTICLE{Torre1977,
-+
+  author = {Jose Garcia De La Torre, V.A. Bloomfield},
-+
+  title = {Hydrodynamic properties of macromolecular complexes. I. Translation},
-+
+  journal = {Biopolymers},
-+
+  year = {1977},
-+
+  volume = {16},
-+
+  pages = {1747-1763},
-+
+@ARTICLE{Kane2000,
-+
+  author = {C. Kane and J. E. Marsden and M. Ortiz and M. West},
-+
+  title = {Variational integrators and the Newmark algorithm for conservative
-+
+        and dissipative mechanical systems},
-+
+  journal = {International Journal for Numerical Methods in Engineering},
-+
+  year = {2000},
-+
+  volume = {49},
-+
+  pages = {1295-1325},
-+
+  number = {10},
-+
+  month = {Dec 10},
-+
+  abstract = {The purpose of this work is twofold. First, we demonstrate analytically
-+
+        that the classical Newmark family as well as related integration
-+
+        algorithms are variational in the sense of the Veselov formulation
-+
+        of discrete mechanics. Such variational algorithms are well known
-+
+        to be symplectic and momentum preserving and to often have excellent
-+
+        global energy behaviour. This analytical result is verified through
-+
+        numerical examples and is believed to be one of the primary reasons
-+
+        that this class of algorithms performs so well. Second, we develop
-+
+        algorithms for mechanical systems with forcing, and in particular,
-+
+        for dissipative systems. In this case, we develop integrators that
-+
+        are based on a discretization of the Lagrange d'Alembert principle
-+
+        as well as on a variational formulation of dissipation. It is demonstrated
-+
+        that these types of structured integrators have good numerical behaviour
-+
+        in terms of obtaining the correct amounts by which the energy changes
-+
+        over the integration run. Copyright (C) 2000 John Wiley & Sons,
-+
+        Ltd.},
-+
+  annote = {373CJ Times Cited:30 Cited References Count:41},
-+
+  issn = {0029-5981},
-+
+  uri = {<Go to ISI>://000165270600004},
-+
+}
-+
+@ARTICLE{Klimov1997,
+  author = {D. K. Klimov and D. Thirumalai},
+  title = {Viscosity dependence of the folding rates of proteins},
+  uri = {<Go to ISI>://A1997XK29300035},
-+
+@ARTICLE{Kol1997,
-+
+  author = {A. Kol and B. B. Laird and B. J. Leimkuhler},
-+
+  title = {A symplectic method for rigid-body molecular simulation},
-+
+  journal = {Journal of Chemical Physics},
-+
+  year = {1997},
-+
+  volume = {107},
-+
+  pages = {2580-2588},
-+
+  number = {7},
-+
+  month = {Aug 15},
-+
+  abstract = {Rigid-body molecular dynamics simulations typically are performed
-+
+        in a quaternion representation. The nonseparable form of the Hamiltonian
-+
+        in quaternions prevents the use of a standard leapfrog (Verlet)
-+
+        integrator, so nonsymplectic Runge-Kutta, multistep, or extrapolation
-+
+        methods are generally used, This is unfortunate since symplectic
-+
+        methods like Verlet exhibit superior energy conservation in long-time
-+
+        integrations. In this article, we describe an alternative method,
-+
+        which we call RSHAKE (for rotation-SHAKE), in which the entire rotation
-+
+        matrix is evolved (using the scheme of McLachlan and Scovel [J.
-+
+        Nonlin. Sci, 16 233 (1995)]) in tandem with the particle positions.
-+
+        We employ a fast approximate Newton solver to preserve the orthogonality
-+
+        of the rotation matrix. We test our method on a system of soft-sphere
-+
+        dipoles and compare with quaternion evolution using a 4th-order
-+
+        predictor-corrector integrator, Although the short-time error of
-+
+        the quaternion algorithm is smaller for fixed time step than that
-+
+        for RSHAKE, the quaternion scheme exhibits an energy drift which
-+
+        is not observed in simulations with RSHAKE, hence a fixed energy
-+
+        tolerance can be achieved by using a larger time step, The superiority
-+
+        of RSHAKE increases with system size. (C) 1997 American Institute
-+
+        of Physics.},
-+
+  annote = {Xq332 Times Cited:11 Cited References Count:18},
-+
+  issn = {0021-9606},
-+
+  uri = {<Go to ISI>://A1997XQ33200046},
-+
+}
-+
+@ARTICLE{Lansac2001,
+  author = {Y. Lansac and M. A. Glaser and N. A. Clark},
+  title = {Microscopic structure and dynamics of a partial bilayer smectic liquid
+  edition = {2nd},
-+
+@ARTICLE{Leimkuhler1999,
-+
+  author = {B. Leimkuhler},
-+
+  title = {Reversible adaptive regularization: perturbed Kepler motion and classical
-+
+        atomic trajectories},
-+
+  journal = {Philosophical Transactions of the Royal Society of London Series
-+
+        a-Mathematical Physical and Engineering Sciences},
-+
+  year = {1999},
-+
+  volume = {357},
-+
+  pages = {1101-1133},
-+
+  number = {1754},
-+
+  month = {Apr 15},
-+
+  abstract = {Reversible and adaptive integration methods based on Kustaanheimo-Stiefel
-+
+        regularization and modified Sundman transformations are applied
-+
+        to simulate general perturbed Kepler motion and to compute classical
-+
+        trajectories of atomic systems (e.g. Rydberg atoms). The new family
-+
+        of reversible adaptive regularization methods also conserves angular
-+
+        momentum and exhibits superior energy conservation and numerical
-+
+        stability in long-time integrations. The schemes are appropriate
-+
+        for scattering, for astronomical calculations of escape time and
-+
+        long-term stability, and for classical and semiclassical studies
-+
+        of atomic dynamics. The components of an algorithm for trajectory
-+
+        calculations are described. Numerical experiments illustrate the
-+
+        effectiveness of the reversible approach.},
-+
+  annote = {199EE Times Cited:11 Cited References Count:48},
-+
+  issn = {1364-503X},
-+
+  uri = {<Go to ISI>://000080466800007},
-+
+}
-+
+@BOOK{Leimkuhler2004,
+  title = {Simulating Hamiltonian Dynamics},
+  publisher = {Cambridge University Press},
+  uri = {<Go to ISI>://000234826102043},
-+
+@ARTICLE{Luty1994,
-+
+  author = {B. A. Luty and M. E. Davis and I. G. Tironi and W. F. Vangunsteren},
-+
+  title = {A Comparison of Particle-Particle, Particle-Mesh and Ewald Methods
-+
+        for Calculating Electrostatic Interactions in Periodic Molecular-Systems},
-+
+  journal = {Molecular Simulation},
-+
+  year = {1994},
-+
+  volume = {14},
-+
+  pages = {11-20},
-+
+  number = {1},
-+
+  abstract = {We compare the Particle-Particle Particle-Mesh (PPPM) and Ewald methods
-+
+        for calculating electrostatic interactions in periodic molecular
-+
+        systems. A brief comparison of the theories shows that the methods
-+
+        are very similar differing mainly in the technique which is used
-+
+        to perform the ''k-space'' or mesh calculation. Because the PPPM
-+
+        utilizes the highly efficient numerical Fast Fourier Transform (FFT)
-+
+        method it requires significantly less computational effort than
-+
+        the Ewald method and scale's almost linearly with system size.},
-+
+  annote = {Qf464 Times Cited:50 Cited References Count:20},
-+
+  issn = {0892-7022},
-+
+  uri = {<Go to ISI>://A1994QF46400002},
-+
+}
-+
+@BOOK{Marion1990,
+  title = {Classical Dynamics of Particles and Systems},
+  publisher = {Academic Press},
+  edition = {2rd},
-+
+@ARTICLE{Marsden1998,
-+
+  author = {J. E. Marsden and G. W. Patrick and S. Shkoller},
-+
+  title = {Multisymplectic geometry, variational integrators, and nonlinear
-+
+        PDEs},
-+
+  journal = {Communications in Mathematical Physics},
-+
+  year = {1998},
-+
+  volume = {199},
-+
+  pages = {351-395},
-+
+  number = {2},
-+
+  month = {Dec},
-+
+  abstract = {This paper presents a geometric-variational approach to continuous
-+
+        and discrete mechanics and field theories. Using multisymplectic
-+
+        geometry, we show that the existence of the fundamental geometric
-+
+        structures as well as their preservation along solutions can be
-+
+        obtained directly from the variational principle. In particular,
-+
+        we prove that a unique multisymplectic structure is obtained by
-+
+        taking the derivative of an action function, and use this structure
-+
+        to prove covariant generalizations of conservation of symplecticity
-+
+        and Noether's theorem. Natural discretization schemes for PDEs,
-+
+        which have these important preservation properties, then follow
-+
+        by choosing a discrete action functional. In the case of mechanics,
-+
+        we recover the variational symplectic integrators of Veselov type,
-+
+        while for PDEs we obtain covariant spacetime integrators which conserve
-+
+        the corresponding discrete multisymplectic form as well as the discrete
-+
+        momentum mappings corresponding to symmetries. We show that the
-+
+        usual notion of symplecticity along an infinite-dimensional space
-+
+        of fields can be naturally obtained by making a spacetime split.
-+
+        All of the aspects of our method are demonstrated with a nonlinear
-+
+        sine-Gordon equation, including computational results and a comparison
-+
+        with other discretization schemes.},
-+
+  annote = {154RH Times Cited:88 Cited References Count:36},
-+
+  issn = {0010-3616},
-+
+  uri = {<Go to ISI>://000077902200006},
-+
+}
-+
+@ARTICLE{McLachlan1993,
+  author = {R.~I McLachlan},
+  title = {Explicit Lie-Poisson integration and the Euler equations},
+  pages = {3043-3046},
-+
+@ARTICLE{McLachlan1998a,
-+
+  author = {R. I. McLachlan and G. R. W. Quispel},
-+
+  title = {Generating functions for dynamical systems with symmetries, integrals,
-+
+        and differential invariants},
-+
+  journal = {Physica D},
-+
+  year = {1998},
-+
+  volume = {112},
-+
+  pages = {298-309},
-+
+  number = {1-2},
-+
+  month = {Jan 15},
-+
+  abstract = {We give a survey and some new examples of generating functions for
-+
+        systems with symplectic structure, systems with a first integral,
-+
+        systems that preserve volume, and systems with symmetries and/or
-+
+        time-reversing symmetries. Both ODEs and maps are treated, and we
-+
+        discuss how generating functions may be used in the structure-preserving
-+
+        numerical integration of ODEs with the above properties.},
-+
+  annote = {Yt049 Times Cited:7 Cited References Count:26},
-+
+  issn = {0167-2789},
-+
+  uri = {<Go to ISI>://000071558900021},
-+
+}
-+
-+
+@ARTICLE{McLachlan1998,
-+
+  author = {R. I. McLachlan and G. R. W. Quispel and G. S. Turner},
-+
+  title = {Numerical integrators that preserve symmetries and reversing symmetries},
-+
+  journal = {Siam Journal on Numerical Analysis},
-+
+  year = {1998},
-+
+  volume = {35},
-+
+  pages = {586-599},
-+
+  number = {2},
-+
+  month = {Apr},
-+
+  abstract = {We consider properties of flows, the relationships between them, and
-+
+        whether numerical integrators can be made to preserve these properties.
-+
+        This is done in the context of automorphisms and antiautomorphisms
-+
+        of a certain group generated by maps associated to vector fields.
-+
+        This new framework unifies several known constructions. We also
-+
+        use the concept of #covariance# of a numerical method with respect
-+
+        to a group of coordinate transformations. The main application is
-+
+        to explore the relationship between spatial symmetries, reversing
-+
+        symmetries, and time symmetry of flows and numerical integrators.},
-+
+  annote = {Zc449 Times Cited:14 Cited References Count:33},
-+
+  issn = {0036-1429},
-+
+  uri = {<Go to ISI>://000072580500010},
-+
+}
-+
+@ARTICLE{McLachlan2005,
+  author = {R. I. McLachlan and A. Zanna},
+  title = {The discrete Moser-Veselov algorithm for the free rigid body, revisited},
+  annote = {491UW Times Cited:48 Cited References Count:25},
+  issn = {0021-9606},
+  uri = {<Go to ISI>://000172129300049},
-+
+}
-+
-+
+@BOOK{Olver1986,
-+
+  title = {Applications of Lie groups to differential equatitons},
-+
+  publisher = {Springer},
-+
+  year = {1986},
-+
+  author = {P.J. Olver},
-+
+  address = {New York},
-+
+}
-+
-+
+@ARTICLE{Omelyan1998,
-+
+  author = {I. P. Omelyan},
-+
+  title = {On the numerical integration of motion for rigid polyatomics: The
-+
+        modified quaternion approach},
-+
+  journal = {Computers in Physics},
-+
+  year = {1998},
-+
+  volume = {12},
-+
+  pages = {97-103},
-+
+  number = {1},
-+
+  month = {Jan-Feb},
-+
+  abstract = {A revised version of the quaternion approach for numerical integration
-+
+        of the equations of motion for rigid polyatomic molecules is proposed.
-+
+        The modified approach is based on a formulation of the quaternion
-+
+        dynamics with constraints. This allows one to resolve the rigidity
-+
+        problem rigorously using constraint forces. It is shown that the
-+
+        procedure for preservation of molecular rigidity can be realized
-+
+        particularly simply within the Verlet algorithm in velocity form.
-+
+        We demonstrate that the method presented leads to an improved numerical
-+
+        stability with respect to the usual quaternion rescaling scheme
-+
+        and it is roughly as good as the cumbersome atomic-constraint technique.
-+
+        (C) 1998 American Institute of Physics.},
-+
+  annote = {Yx279 Times Cited:12 Cited References Count:28},
-+
+  issn = {0894-1866},
-+
+  uri = {<Go to ISI>://000072024300025},
-+
+@ARTICLE{Omelyan1998a,
-+
+  author = {I. P. Omelyan},
-+
+  title = {Algorithm for numerical integration of the rigid-body equations of
-+
+        motion},
-+
+  journal = {Physical Review E},
-+
+  year = {1998},
-+
+  volume = {58},
-+
+  pages = {1169-1172},
-+
+  number = {1},
-+
+  month = {Jul},
-+
+  abstract = {An algorithm for numerical integration of the rigid-body equations
-+
+        of motion is proposed. The algorithm uses the leapfrog scheme and
-+
+        the quantities involved are angular velocities and orientational
-+
+        variables that can be expressed in terms of either principal axes
-+
+        or quaternions. Due to specific features of the algorithm, orthonormality
-+
+        and unit norms of the orientational variables are integrals of motion,
-+
+        despite an approximate character of the produced trajectories. It
-+
+        is shown that the method presented appears to be the most efficient
-+
+        among all such algorithms known.},
-+
+  annote = {101XL Times Cited:8 Cited References Count:22},
-+
+  issn = {1063-651X},
-+
+  uri = {<Go to ISI>://000074893400151},
-+
+}
-+
+@ARTICLE{Orlandi2006,
+  author = {S. Orlandi and R. Berardi and J. Steltzer and C. Zannoni},
+  title = {A Monte Carlo study of the mesophases formed by polar bent-shaped
+  uri = {<Go to ISI>://000236464000072},
-+
+@ARTICLE{Owren1992,
-+
+  author = {B. Owren and M. Zennaro},
-+
+  title = {Derivation of Efficient, Continuous, Explicit Runge-Kutta Methods},
-+
+  journal = {Siam Journal on Scientific and Statistical Computing},
-+
+  year = {1992},
-+
+  volume = {13},
-+
+  pages = {1488-1501},
-+
+  number = {6},
-+
+  month = {Nov},
-+
+  abstract = {Continuous, explicit Runge-Kutta methods with the minimal number of
-+
+        stages are considered. These methods are continuously differentiable
-+
+        if and only if one of the stages is the FSAL evaluation. A characterization
-+
+        of a subclass of these methods is developed for orders 3, 4, and
-+
+. It is shown how the free parameters of these methods can be used
-+
+        either to minimize the continuous truncation error coefficients
-+
+        or to maximize the stability region. As a representative for these
-+
+        methods the fifth-order method with minimized error coefficients
-+
+        is chosen, supplied with an error estimation method, and analysed
-+
+        by using the DETEST software. The results are compared with a similar
-+
+        implementation of the Dormand-Prince 5(4) pair with interpolant,
-+
+        showing a significant advantage in the new method for the chosen
-+
+        problems.},
-+
+  annote = {Ju936 Times Cited:25 Cited References Count:20},
-+
+  issn = {0196-5204},
-+
+  uri = {<Go to ISI>://A1992JU93600013},
-+
+}
-+
+@ARTICLE{Palacios1998,
+  author = {J. L. Garcia-Palacios and F. J. Lazaro},
+  title = {Langevin-dynamics study of the dynamical properties of small magnetic
+  annote = {Akb93 Times Cited:71 Cited References Count:12},
+  issn = {0021-9991},
+  uri = {<Go to ISI>://A1985AKB9300008},
-+
+}
-+
-+
+@ARTICLE{Rotne1969,
-+
+  author = {F. Perrin},
-+
+  title = {Variational treatment of hydrodynamic interaction in polymers},
-+
+  journal = {J. Chem. Phys.},
-+
+  year = {1969},
-+
+  volume = {50},
-+
+  pages = {4831�C4837},
-+
+}
-+
-+
+@ARTICLE{Perrin1936,
-+
+  author = {F. Perrin},
-+
+  title = {Mouvement brownien d'un ellipsoid(II). Rotation libre et depolarisation
-+
+        des fluorescences. Translation et diffusion de moleculese ellipsoidales},
-+
+  journal = {J. Phys. Radium},
-+
+  year = {1936},
-+
+  volume = {7},
-+
+  pages = {1-11},
-+
+}
-+
-+
+@ARTICLE{Perrin1934,
-+
+  author = {F. Perrin},
-+
+  title = {Mouvement brownien d'un ellipsoid(I). Dispersion dielectrique pour
-+
+        des molecules ellipsoidales},
-+
+  journal = {J. Phys. Radium},
-+
+  year = {1934},
-+
+  volume = {5},
-+
+  pages = {497-511},
+@ARTICLE{Petrache1998,
+  uri = {<Go to ISI>://000235990500001},
-+
+@ARTICLE{Reich1999,
-+
+  author = {S. Reich},
-+
+  title = {Backward error analysis for numerical integrators},
-+
+  journal = {Siam Journal on Numerical Analysis},
-+
+  year = {1999},
-+
+  volume = {36},
-+
+  pages = {1549-1570},
-+
+  number = {5},
-+
+  month = {Sep 8},
-+
+  abstract = {Backward error analysis has become an important tool for understanding
-+
+        the long time behavior of numerical integration methods. This is
-+
+        true in particular for the integration of Hamiltonian systems where
-+
+        backward error analysis can be used to show that a symplectic method
-+
+        will conserve energy over exponentially long periods of time. Such
-+
+        results are typically based on two aspects of backward error analysis:
-+
+        (i) It can be shown that the modified vector fields have some qualitative
-+
+        properties which they share with the given problem and (ii) an estimate
-+
+        is given for the difference between the best interpolating vector
-+
+        field and the numerical method. These aspects have been investigated
-+
+        recently, for example, by Benettin and Giorgilli in [J. Statist.
-+
+        Phys., 74 (1994), pp. 1117-1143], by Hairer in [Ann. Numer. Math.,
-+
+(1994), pp. 107-132], and by Hairer and Lubich in [Numer. Math.,
-+
+(1997), pp. 441-462]. In this paper we aim at providing a unifying
-+
+        framework and a simplification of the existing results and corresponding
-+
+        proofs. Our approach to backward error analysis is based on a simple
-+
+        recursive definition of the modified vector fields that does not
-+
+        require explicit Taylor series expansion of the numerical method
-+
+        and the corresponding flow maps as in the above-cited works. As
-+
+        an application we discuss the long time integration of chaotic Hamiltonian
-+
+        systems and the approximation of time averages along numerically
-+
+        computed trajectories.},
-+
+  annote = {237HV Times Cited:43 Cited References Count:41},
-+
+  issn = {0036-1429},
-+
+  uri = {<Go to ISI>://000082650600010},
-+
+}
-+
+@ARTICLE{Ros2005,
+  author = {M. B. Ros and J. L. Serrano and M. R. {de la Fuente} and C. L. Folcia},
+  title = {Banana-shaped liquid crystals: a new field to explore},
+  annote = {985FW Times Cited:0 Cited References Count:30},
+  issn = {1292-8941},
+  uri = {<Go to ISI>://000233363300002},
-+
+}
-+
-+
+@ARTICLE{Ryckaert1977,
-+
+  author = {J. P. Ryckaert and G. Ciccotti and H. J. C. Berendsen},
-+
+  title = {Numerical-Integration of Cartesian Equations of Motion of a System
-+
+        with Constraints - Molecular-Dynamics of N-Alkanes},
-+
+  journal = {Journal of Computational Physics},
-+
+  year = {1977},
-+
+  volume = {23},
-+
+  pages = {327-341},
-+
+  number = {3},
-+
+  annote = {Cz253 Times Cited:3680 Cited References Count:7},
-+
+  issn = {0021-9991},
-+
+  uri = {<Go to ISI>://A1977CZ25300007},
-+
+@ARTICLE{Sagui1999,
-+
+  author = {C. Sagui and T. A. Darden},
-+
+  title = {Molecular dynamics simulations of biomolecules: Long-range electrostatic
-+
+        effects},
-+
+  journal = {Annual Review of Biophysics and Biomolecular Structure},
-+
+  year = {1999},
-+
+  volume = {28},
-+
+  pages = {155-179},
-+
+  abstract = {Current computer simulations of biomolecules typically make use of
-+
+        classical molecular dynamics methods, as a very large number (tens
-+
+        to hundreds of thousands) of atoms are involved over timescales
-+
+        of many nanoseconds. The methodology for treating short-range bonded
-+
+        and van der Waals interactions has matured. However, long-range
-+
+        electrostatic interactions still represent a bottleneck in simulations.
-+
+        In this article, we introduce the basic issues for an accurate representation
-+
+        of the relevant electrostatic interactions. In spite of the huge
-+
+        computational time demanded by most biomolecular systems, it is
-+
+        no longer necessary to resort to uncontrolled approximations such
-+
+        as the use of cutoffs. In particular, we discuss the Ewald summation
-+
+        methods, the fast particle mesh methods, and the fast multipole
-+
+        methods. We also review recent efforts to understand the role of
-+
+        boundary conditions in systems with long-range interactions, and
-+
+        conclude with a short perspective on future trends.},
-+
+  annote = {213KJ Times Cited:126 Cited References Count:73},
-+
+  issn = {1056-8700},
-+
+  uri = {<Go to ISI>://000081271400008},
-+
+}
-+
+@ARTICLE{Sandu1999,
+  author = {A. Sandu and T. Schlick},
+  title = {Masking resonance artifacts in force-splitting methods for biomolecular
+  uri = {<Go to ISI>://000227296700019},
-+
+@ARTICLE{Shimada1993,
-+
+  author = {J. Shimada and H. Kaneko and T. Takada},
-+
+  title = {Efficient Calculations of Coulombic Interactions in Biomolecular
-+
+        Simulations with Periodic Boundary-Conditions},
-+
+  journal = {Journal of Computational Chemistry},
-+
+  year = {1993},
-+
+  volume = {14},
-+
+  pages = {867-878},
-+
+  number = {7},
-+
+  month = {Jul},
-+
+  abstract = {To make improved treatments of electrostatic interactions in biomacromolecular
-+
+        simulations, two possibilities are considered. The first is the
-+
+        famous particle-particle and particle-mesh (PPPM) method developed
-+
+        by Hockney and Eastwood, and the second is a new one developed here
-+
+        in their spirit but by the use of the multipole expansion technique
-+
+        suggested by Ladd. It is then numerically found that the new PPPM
-+
+        method gives more accurate results for a two-particle system at
-+
+        small separation of particles. Preliminary numerical examination
-+
+        of the various computational methods for a single configuration
-+
+        of a model BPTI-water system containing about 24,000 particles indicates
-+
+        that both of the PPPM methods give far more accurate values with
-+
+        reasonable computational cost than do the conventional truncation
-+
+        methods. It is concluded the two PPPM methods are nearly comparable
-+
+        in overall performance for the many-particle systems, although the
-+
+        first method has the drawback that the accuracy in the total electrostatic
-+
+        energy is not high for configurations of charged particles randomly
-+
+        generated.},
-+
+  annote = {Lh164 Times Cited:27 Cited References Count:47},
-+
+  issn = {0192-8651},
-+
+  uri = {<Go to ISI>://A1993LH16400011},
-+
+}
-+
+@ARTICLE{Skeel2002,
+  author = {R. D. Skeel and J. A. Izaguirre},
+  title = {An impulse integrator for Langevin dynamics},
+  uri = {<Go to ISI>://A1992JE89100044},
-+
+@BOOK{Varadarajan1974,
-+
+  title = {Lie groups, Lie algebras, and their representations},
-+
+  publisher = {Prentice-Hall},
-+
+  year = {1974},
-+
+  author = {V.S. Varadarajan},
-+
+  address = {New York},
-+
+}
-+
+@ARTICLE{Wegener1979,
+  author = {W.~A. Wegener, V.~J. Koester and R.~M. Dowben},
+  title = {A general ellipsoid can not always serve as a modle for the rotational
+  uri = {<Go to ISI>://000186273200027},
-+
+@ARTICLE{Wolf1999,
-+
+  author = {D. Wolf and P. Keblinski and S. R. Phillpot and J. Eggebrecht},
-+
+  title = {Exact method for the simulation of Coulombic systems by spherically
-+
+        truncated, pairwise r(-1) summation},
-+
+  journal = {Journal of Chemical Physics},
-+
+  year = {1999},
-+
+  volume = {110},
-+
+  pages = {8254-8282},
-+
+  number = {17},
-+
+  month = {May 1},
-+
+  abstract = {Based on a recent result showing that the net Coulomb potential in
-+
+        condensed ionic systems is rather short ranged, an exact and physically
-+
+        transparent method permitting the evaluation of the Coulomb potential
-+
+        by direct summation over the r(-1) Coulomb pair potential is presented.
-+
+        The key observation is that the problems encountered in determining
-+
+        the Coulomb energy by pairwise, spherically truncated r(-1) summation
-+
+        are a direct consequence of the fact that the system summed over
-+
+        is practically never neutral. A simple method is developed that
-+
+        achieves charge neutralization wherever the r(-1) pair potential
-+
+        is truncated. This enables the extraction of the Coulomb energy,
-+
+        forces, and stresses from a spherically truncated, usually charged
-+
+        environment in a manner that is independent of the grouping of the
-+
+        pair terms. The close connection of our approach with the Ewald
-+
+        method is demonstrated and exploited, providing an efficient method
-+
+        for the simulation of even highly disordered ionic systems by direct,
-+
+        pairwise r(-1) summation with spherical truncation at rather short
-+
+        range, i.e., a method which fully exploits the short-ranged nature
-+
+        of the interactions in ionic systems. The method is validated by
-+
+        simulations of crystals, liquids, and interfacial systems, such
-+
+        as free surfaces and grain boundaries. (C) 1999 American Institute
-+
+        of Physics. [S0021-9606(99)51517-1].},
-+
+  annote = {189PD Times Cited:70 Cited References Count:34},
-+
+  issn = {0021-9606},
-+
+  uri = {<Go to ISI>://000079913000008},
-+
+}
-+
-+
+@ARTICLE{Yoshida1990,
-+
+  author = {H. Yoshida},
-+
+  title = {Construction of Higher-Order Symplectic Integrators},
-+
+  journal = {Physics Letters A},
-+
+  year = {1990},
-+
+  volume = {150},
-+
+  pages = {262-268},
-+
+  number = {5-7},
-+
+  month = {Nov 12},
-+
+  annote = {Ej798 Times Cited:492 Cited References Count:9},
-+
+  issn = {0375-9601},
-+
+  uri = {<Go to ISI>://A1990EJ79800009},
-+
+}
-+

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Revision 2786 by tim, Sun Jun 4 20:18:07 2006 UTC vs.
Revision 2789 by tim, Mon Jun 5 21:00:46 2006 UTC