The Experts below are selected from a list of 5993472 Experts worldwide ranked by ideXlab platform
M V Tretyakov - One of the best experts on this subject based on the ideXlab platform.
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new langevin and gradient thermostats for rigid body dynamics
Journal of Chemical Physics, 2015Co-Authors: Ruslan L Davidchack, Thomas E Ouldridge, M V TretyakovAbstract:We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical Integrators for the Langevin thermostat and one for the gradient thermostat. The numerical Integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin Integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin Integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type Integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin Integrators, as well as the efficiency of the gradient Integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient Integrator is computationally less efficient than the Langevin Integrators. We also compare the relative accuracy of the Langevin Integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate Integrator.
Melvin Leok - One of the best experts on this subject based on the ideXlab platform.
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Lagrangian and Hamiltonian Taylor variational Integrators
BIT Numerical Mathematics, 2018Co-Authors: Jeremy Schmitt, Tatiana Shingel, Melvin LeokAbstract:In this paper, we present a variational Integrator that is based on an approximation of the Euler–Lagrange boundary-value problem via Taylor’s method. This can be viewed as a special case of the shooting-based variational Integrator. The Taylor variational Integrator exploits the structure of the Taylor method, which results in a shooting method that is one order higher compared to other shooting methods based on a one-step method of the same order. In addition, this method can generate quadrature nodal evaluations at the cost of a polynomial evaluation, which may increase its efficiency relative to other shooting-based variational Integrators. A symmetric version of the method is proposed, and numerical experiments are conducted to exhibit the efficacy and efficiency of the method.
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Lie Group Spectral Variational Integrators
Foundations of Computational Mathematics, 2017Co-Authors: James Hall, Melvin LeokAbstract:We present a new class of high-order variational Integrators on Lie groups. We show that these Integrators are symplectic and momentum-preserving, can be constructed to be of arbitrarily high order, or can be made to converge geometrically. Furthermore, these methods are capable of taking very large time-steps. We demonstrate the construction of one such variational Integrator for the rigid body and discuss how this construction could be generalized to other related Lie group problems. We close with several numerical examples which demonstrate our claims and discuss further extensions of our work.
Franco Maloberti - One of the best experts on this subject based on the ideXlab platform.
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FEED-FORWARD PATH AND GAIN-SCALING – A SWING AND DISTORTION REDUCTION SCHEME FOR SECOND ORDER SIGMA-DELTA MODULATOR
2016Co-Authors: Wern Ming Koe, Franco MalobertiAbstract:This paper proposed two second-order sigma-delta modulator schemes for reducing the swing at the output of the first and the second Integrators. The new schemes used feed-forward path to eliminate the term due to the input signal at the output of the first and second Integrators completely. Hence, the Integrators are processing only the quantization noise that is uncorrelated to the input signal. This paper also proposed a condition for scaling each Integrator gain to further reduce the first Integrator output swing using gain-scaling technique. Both techniques will make the modulator less sensitive to any harmonic distortion from the opamp used in the Integrator. 1
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feed forward path and gain scaling a swing and distortion reduction scheme for second order sigma delta modulator
International Symposium on Circuits and Systems, 2004Co-Authors: Wern Ming Koe, Franco MalobertiAbstract:This paper proposed a two second-order sigma-delta modulator schemes for reducing the swing at the output of the first and the second Integrators. The new schemes used feed-forward path to eliminate the term due to the input signal at the output of the first and second Integrators completely. Hence, the Integrators are processing only the quantization noise that is uncorrelated to the input signal. This paper also proposed a condition for scaling each Integrator gain to further reduce the first Integrator output swing using gain-scaling technique. Both techniques will make the modulator less sensitive to any harmonic distortion from the opamp used in the Integrator.
Ruslan L Davidchack - One of the best experts on this subject based on the ideXlab platform.
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new langevin and gradient thermostats for rigid body dynamics
Journal of Chemical Physics, 2015Co-Authors: Ruslan L Davidchack, Thomas E Ouldridge, M V TretyakovAbstract:We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical Integrators for the Langevin thermostat and one for the gradient thermostat. The numerical Integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin Integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin Integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type Integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin Integrators, as well as the efficiency of the gradient Integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient Integrator is computationally less efficient than the Langevin Integrators. We also compare the relative accuracy of the Langevin Integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate Integrator.
Ghyslain Gagnon - One of the best experts on this subject based on the ideXlab platform.
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Dynamic range scaling of sigma-delta modulators based on a multi-criteria optimization process
2011 IEEE 9th International New Circuits and systems conference, 2011Co-Authors: Etienne Collard-frechette, Georges Kaddoum, Ghyslain GagnonAbstract:This paper presents a new coefficient scaling technique to determine the dynamic range of the Integrators of sigma delta modulators. This technique relies on numerical optimization of the interstage coefficients to minimize a multi-criteria objective function taking into account the sum of capacitor values implementing the modulator and the voltage swing at each Integrator output, for a given target SNR. The optimization process includes the effect of thermal noise at each Integrator stage. A user-defined parameter can steer the optimization process priority towards either the size of the capacitors or the Integrators output voltage swing, depending on the given application.
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a new optimization technique for coefficient scaling in sigma delta modulators
International Midwest Symposium on Circuits and Systems, 2010Co-Authors: Etienne Collardfrechette, Ghyslain GagnonAbstract:This article proposes a new method for scaling the output swing of the Integrators in a sigma-delta modulator. The algorithm takes in consideration the relative effect on the output signal-to-noise ratio of the thermal noise from each Integrator to find a set of coefficients which implements the desired transfer functions while reducing the signal swing at each node. Simulation results show that the last two Integrators output swing can be reduced by 50% and 90% respectively for a 0.5 dB signal-to-noise ratio reduction.
