a semi analytical approach to molecular dynamics despite numerous computational advances over the last few decades molecular dynamics still favors explicit and thus easily parallelizable time integrators for large scale numerical simulation as a consequence computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size in this paper we present a semi analytical integration scheme that offers a total speedup of a factor 30 compared to the verlet method on typical md simulation by allowing over three orders of magnitude larger step sizes by efficiently approximating the exact integration of the strong harmonic forces of covalent bonds through matrix functions far improved stability with respect to time step size is achieved without sacrificing the explicit symplectic time reversible or fine grained parallelizable nature of the integration scheme we demonstrate the efficiency and scalability of our integrator on simulations ranging from dna strand unbinding and protein folding to nanotube resonators

brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

shadow hybrid monte carlo an efficient propagator in phase space of macromolecules shadow hybrid monte carlo shmc is a new method for sampling the phase space of large molecules particularly biological molecules it improves sampling of hybrid monte carlo hmc by allowing larger time steps and system sizes in the molecular dynamics md step the acceptance rate of hmc decreases exponentially with increasing system size n or time step t this is due to discretization errors introduced by the numerical integrator shmc achieves an asymptotic o n1 4 speedup over hmc by sampling from all of phase space using high order approximations to a shadow or modified hamiltonian exactly integrated by a symplectic md integrator shmc satisfies microscopic reversibility and is a rigorous sampling method shmc requires extra storage modest computational overhead and a reweighting step to obtain averages from the canonical ensemble this is validated by numerical experiments that compute observables for different molecules ranging from a small n alkane butane with four united atoms to a larger solvated protein with 14 281 atoms in these experiments shmc achieves an order magnitude speedup in sampling efficiency for medium sized proteins sampling efficiency is measured by monitoring the rate at which different conformations of the molecules dihedral angles are visited and by computing ergodic measures of some observables

a compactness lemma for quasilinear problems application to parabolic equations in this paper we solve the problem ut au f u u and u 0 u0 where and u0 are bounded radon measures the method is based upon three fundamental lemmas a compactness result lemma 3 a regularity result lemma 7 and an integration by parts lemma 2

vanishing shear viscosity in a free boundary problem for the equations of compressible fluids abstract a free boundary problem of describing a joint motion of two compressible fluids with different viscosities is considered the passage to the limit is studied as the shear viscosity of one of the fluids vanishes

variational integrators for electric circuits in this contribution we develop a variational integrator for the simulation of stochastic and multiscale electric circuits when considering the dynamics of an electric circuit one is faced with three special situations 1 the system involves external control forcing through external controlled voltage sources and resistors 2 the system is constrained via the kirchhoff current kcl and voltage laws kvl 3 the lagrangian is degenerate based on a geometric setting an appropriate variational formulation is presented to model the circuit from which the equations of motion are derived a time discrete variational formulation provides an iteration scheme for the simulation of the electric circuit dependent on the discretization the intrinsic degeneracy of the system can be canceled for the discrete variational scheme in this way a variational integrator is constructed that gains several advantages compared to standard integration tools for circuits in particular a comparison to bdf methods which are usually the method of choice for the simulation of electric circuits shows that even for simple lcr circuits a better energy behavior and frequency spectrum preservation can be observed using the developed variational integrator

numerical algorithms for highly oscillatory dynamic system based on commutator free method in the present paper an efficiently improved modified magnus integrator algorithm based on commutator free method is proposed for the second order dynamic systems with time dependent high frequencies firstly the second order dynamic systems are transferred to the frame of reference by introducing new variable so that highly oscillatory behaviour inherited from the entries then the modified magnus integrator method based on local linearization is appropriately designed for solving the above new form and some optimized strategies for reducing the number of function evaluations and matrix operations are also suggested finally several numerical examples for highly oscillatory dynamic systems such as airy equation bessel equation mathieu equation are presented to demonstrate the validity and effectiveness of the proposed method

identification of fuzzy relational model and its application to control abstract in the case of control systems where physical mechanisms are not well known due to high complexity and nonlinearity a fuzzy relational model may be useful in this paper we propose a recursive parameter tuning algorithm for the identification of fuzzy relational model for an unknown dynamic system furthermore using the fact that a dynamic system is represented by the relational strength between a few reference input and output fuzzy sets in the fuzzy relational model we construct a control input fuzzy set inducing a desired output fuzzy set by calculating the possibility between the model output and the desired output fuzzy set for the control purpose simulation results show the usefulness of the proposed identification and control algorithms

a stochastic immersed boundary method for fluid structure dynamics at microscopic length scales in modeling many biological systems it is important to take into account flexible structures which interact with a fluid at the length scale of cells and cell organelles thermal fluctuations of the aqueous environment become significant in this work it is shown how the immersed boundary method of c s peskin the immersed boundary method acta num 11 2002 1 39 for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations a stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps an important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved partially resolved or fully resolved while retaining a good level of accuracy error estimates in each of these regimes are given for the method a number of theoretical and numerical checks are furthermore performed to assess its physical fidelity for a conservative force the method is found to simulate particles with the correct boltzmann equilibrium statistics it is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters the method is also shown to reproduce a well known hydrodynamic effect of a brownian particle in which the velocity autocorrelation function exhibits an algebraic 3 2 decay for long times b j alder t e wainwright decay of the velocity autocorrelation function phys rev a 1 1 1970 18 21 a few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method specifically we present simulations of osmotic effects of molecular dimers worm like chain polymer knots and a basic model of a molecular motor immersed in fluid subject to a hydrodynamic load force the theoretical analysis and numerical results show that the immersed boundary method with thermal fluctuations captures many important features of small length scale hydrodynamic systems and holds promise as an effective method for simulating biological phenomena on the cellular and subcellular length scales

exact differentiation and sliding mode observers for switched lagrangian systems abstract the main topic of this paper is the problem of constructing observers for switched mechanical systems which includes as a specific case the design of observers based on the high order sliding mode technique the high order sliding mode is used to overcome the chattering phenomena occurring which induce some irrelevant and undesirable phenomena for mechanical systems the proposed approach based on the fliess canonical form also allows observers to give an estimate of the discrete location of the system which indicates the dynamic evolution the convergence of the observers is proved and a stick mass friction system is used to illustrate the efficiency of the proposed hybrid observers

efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form for hybrid systems described by switched linear difference equations linear threshold conditions automata and propositional logic conditions described in mixed logical dynamical form this note describes two algorithms for transforming such systems into an equivalent piecewise affine form where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical the proposed techniques exploit ideas from mixed integer programming and multiparametric programming

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

on error bounds for the gautschi type exponential integrator applied to oscillatory second order differential equations this paper studies a numerical method for second order oscillatory differential equations in which high frequency oscillations are generated by a linear time and or solution dependent part for constant linear part it is known that the method allows second order error bounds independent of the product of the step size with the frequencies and is therefore a long time step method most real world problems are not of that kind and it is important to study more general equations the analysis in this paper shows that one obtains second order error bounds even in the case of a time and or solution dependent linear part if the matrix is evaluated at averaged positions

long time energy conservation of numerical methods for oscillatory differential equations we consider second order differential systems where high frequency oscillations are generated by a linear part we present a frequency expansion of the solution and we discuss two invariants of the system that determine the coefficients of the frequency expansion these invariants are related to the total energy and the oscillatory harmonic energy of the original system for the numerical solution we study a class of symmetric methods that discretize the linear part without error we are interested in the case where the product of the step size with the highest frequency can be large in the sense of backward error analysis we represent the numerical solution by a frequency expansion where the coefficients are the solution of a modified system this allows us to prove the near conservation of the total and the oscillatory energy over very long time intervals

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

introducing the fuzzy relational hybrid model as a building block for intelligent modeling of hybrid dynamical systems in this paper a novel intelligent modeling framework is introduced for modeling hybrid dynamical systems which may contain both continuous valued and discrete valued dynamics and or signals the proposed modeling framework consists of a fuzzy relational hybrid model frhm structure and an online identification algorithm the frhm structure has some useful properties e g the ability of modeling both hard and soft switchings even simultaneously model transparency in view of knowledge extraction and knowledge embedment and possibility of connecting disjoint models through mathematical operations to construct larger model structures in addition the proposed frhm structure can be used to model a wide variety of hybrid dynamical systems including nonlinear dynamical systems dynamical systems with switchings or logical functions dynamical systems with discrete valued or qualitative inputs and or outputs etc the fuzzy relational hybrid dynamical system is an important product of the proposed modeling structure which in this paper has applied to modeling an asynchronous dc dc buck converter as the case study

long time step methods for oscillatory differential equations considered are numerical integration schemes for nondissipative dynamical systems in which multiple time scales are present it is assumed that one can do an explicit separation of the rhs forces into fast forces and slow forces such that i the fast forces contain the high frequency part of the solution ii the fast forces are conservative and iii the reduced problem consisting only of the fast forces can be integrated much more cheaply than the full problem the fast forces are allowed to have low frequency components particular applications for which the schemes are intended include n body problems for which most of the forces are slow and nonlinear wave phenomena for which the fast forces can be propagated by spectral methods the assumption of cheap integration of fast forces implies that the overall cost of integration is primarily determined by the step size used to sample the slow forces a long time step method is one in which this step size exceeds half the period of the fastest normal mode present in the full system an existing method that comes close to qualifying is the impulse method also known as verlet i and r respa it is shown that it might fail though for a couple of reasons first it suffers a serious loss of accuracy if the step size is near a multiple of the period of a normal mode and second it is unstable if the step size is near a multiple of half the period of a normal mode proposed in this paper is a mollified impulse method having an error bound that is independent of the frequency of the fast forces it is also shown to possess superior stability properties theoretical results are supplemented by numerical experiments the method is efficient and reasonably easy to implement

mpc for continuous piecewise affine systems abstract a large class of hybrid systems can be described by a max min plus scaling mmps model i e using the operations maximization minimization addition and scalar multiplication first we show that continuous piecewise affine systems are equivalent to mmps systems next we consider model predictive control mpc for these systems in general this leads to nonlinear nonconvex optimization problems we present a new mpc method for mmps systems that is based on canonical forms for mmps functions in case the mpc constraints are linear constraints in the inputs only this results in a sequence of linear optimization problems such that the mpc control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work

heterogeneous multiscale methods for stiff ordinary differential equations the heterogeneous multiscale methods hmm is a general framework for the numerical approximation of multiscale problems it is here developed for ordinary differential equations containing differe

explicit symplectic integrators using hessian vector products in 1991 rowlands proposed an effectively fourth order effectively two stage explicit symplectic integrator based on using a hessian vector product to modify the force evaluation in the leapfrog method and evidence indicates that for modest accuracy this method is highly competitive here we explore the possible existence of even more efficient fourth order explicit symplectic integrators also based on the use of hessian vector products and the concept of effective order first it is shown that the cost of a force evaluation plus a hessian vector product is less than twice the cost of the force alone for a sum of two body interactions then a new method is found that is generally better than both the method of rowlands and that of calvo according to both a theoretical measure of the error and limited numerical experiments the basic motivation behind the new method is quite simple do a hessian vector computation only every other step significantly cutting costs while only marginally increasing the error the idea of effective order means that we allow for both the possibility of preprocessing the initial values before application of the basic method and the possibility of postprocessing the values obtained by the basic method but at output points only for some applications processing is unnecessary but in any case processing has been shown to be possible at low additional cost the derivation of the new method illustrates how to simplify by the use of h series the determination of parameters for methods of increased effective accuracy