The Experts below are selected from a list of 20274 Experts worldwide ranked by ideXlab platform
Kazunari Kaneko - One of the best experts on this subject based on the ideXlab platform.
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Self-consistent collective coordinate method in nuclear rotation and wobbling motion at high spin
Physical Review C, 1994Co-Authors: Kazunari KanekoAbstract:We propose a method, using the self-consistent collective coordinate method based on the time-dependent Hartree-Bogoliubov theory, to describe nuclear rotation and wobbling motion in triaxially deformed nuclei beyond the random-phase approximation to higher orders. In this perturbation method, the zero modes can be eliminated by imposing constraints to determine the intrinsic Frame: a spin-orientation Frame or a principal Axis Frame. The basic equations on the collective submanifold are derived as canonical conditions and equations of collective submanifold. These equations are solved by an iterative method expanded with collective variables. In lowest order, the basic equations in both the principal-Axis Frame and the spin-orientation Frame lead to the same result as that derived by Marshalek.
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Rotation and wobbling motion in triaxially deformed nuclei
Physical Review C, 1992Co-Authors: Kazunari KanekoAbstract:A quantum mechanical method of rotation and wobbling motion in triaxially deformed nuclei is represented within the Framework of time-dependent Hartree-Fock theory. For such systems, the intrinsic Frame is defined by imposing constraints of principal-Axis Frame. With aid of the canonical formulation of the constrained system, the Dirac quantization of the classical system is performed. It is shown that the commutation relations of angular momentum in the intrinsic Frame then exactly satisfy the body-fixed Frame. Furthermore, a method of describing large amplitude collective motion in the constrained system is proposed by extending the self-consistent collective-coordinate method.
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Beyond RPA in nuclear rotation and wobbling motion at high spin
Physics Letters B, 1991Co-Authors: Kazunari KanekoAbstract:Abstract A quantum mechanical method of the nuclear rotation and the wobbling motion at high spin beyond the small-oscillation approximation is represented within the Framework of time-dependent mean-field theory with some constraints. The constraints which determine the choice of the rotating reference Frame are considered in the spin-orientation Frame and the principal-Axis Frame. The quantization under such constraints is performed by making use of the Dirac bracket. Then the commutation relations of the angular momentum are derived.
Rengarajan Amirtharajan - One of the best experts on this subject based on the ideXlab platform.
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Design, Simulation and Hardware Implementation of Shunt Hybrid Compensator Using Synchronous Rotating Reference Frame (SRRF)-Based Control Technique
Electronics, 2019Co-Authors: R. Balasubramanian, K. Parkavikathirvelu, R Sankaran, Rengarajan AmirtharajanAbstract:This paper deals with the design, simulation, and implementation of shunt hybrid compensator to maintain the power quality in three-phase distribution networks feeding different types balanced and unbalanced nonlinear loads. The configuration of the compensator consists of a selective harmonic elimination passive filter, a series-connected conventional six-pulse IGBT inverter, acting as the active filter terminated with a DC link capacitor. The theory and modelling of the compensator based on current harmonic components at the load end and their decomposition in d-q Axis Frame of reference are utilized in the reference current generation algorithm. Accordingly, the source current waveform is made to follow the reference current waveform using a high-frequency, carrier-based controller. Further, this inner current control loop is supported by a slower outer voltage control loop for sustaining desirable DC link voltage. Performance of the compensator is evaluated through MATLAB simulation covering different types of loads and reduction of harmonic currents and THD at the supply side along with excellent regulation of DC link voltage are confirmed. The performance of a hybrid compensator designed and fabricated using the above principles is evaluated and corroborated with the simulation results.
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Design, Simulation and Hardware Implementation of Shunt Hybrid Compensator using Synchronous Rotating Reference Frame Based Control Technique
2018Co-Authors: Balasubramanian R, Parkavi Kathirvelu K, Sankaran R, Rengarajan AmirtharajanAbstract:This paper deals with the design, simulation and implementation of shunt hybrid compensator to maintain the power quality in 3-phase distribution networks feeding different types balanced and unbalanced nonlinear loads. The configuration of the compensator consists of a selective harmonic elimination passive filter, a series connected conventional 6-pulse IGBT inverter, acting as the active filter terminated with a dc link capacitor. The theory and modelling of the compensator based on current harmonic components at the load end and their decomposition in d-q Axis Frame of reference are utilized in the reference current generation algorithm. Accordingly, the source current waveform is made to follow the reference current waveform using a high frequency carrier based controller. Further, this inner current control loop is supported by a slower outer voltage control loop for sustaining desirable dc link voltage. Performance of the compensator is evaluated through MATLAB simulation covering different types of loads and reduction of harmonic currents and THD at the supply side along with excellent regulation of dc link voltage are confirmed. The performance of a hybrid compensator designed and fabricated using the above principles is evaluated and corroborated with the simulation results.
David Cowburn - One of the best experts on this subject based on the ideXlab platform.
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Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination.
Journal of Biomolecular NMR, 2017Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract:We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-Axis-Frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing Framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms—RDC-SOS and RDC–NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramer–Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.
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Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract:We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program. Often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-Axis-Frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing Framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy. The two algorithms - RDC-SOS and RDC-NOE-SOS, have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. We introduce a statistical tool, the Cramer-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any methodology. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements, achieving more accurate and faster reconstructions compared to the current state of the art.
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Integrating NOE and RDC using semidefinite programming for protein structure determination
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract:We revisit the established problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, in practice the distance restraints are imprecise, and sometimes sparse, for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-Axis-Frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing Framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. We estimate the rotation of each rigid unit using SDP relaxation that incorporates chirality constraints. The two SDP based methods we propose - RDC-SDP and RDC-NOE-SDP have polynomial time complexity in the number of amino-acids and run efficiently on a regular PC. We further introduce a statistical tool, the Cram\'er-Rao bound (CRB) to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise, for realistic noise magnitude our SDP algorithm attains the CRB. Through such comparison, the utility of CRB for benchmarking other procedures for structure determination in NMR is demonstrated. Finally, we apply our proposed method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental distance restraints and RDC measurements obtained in two alignment media.
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Residual Dipolar Coupling, Protein Backbone Conformation and Semidefinite Programming.
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract:We investigate the classical problem of protein structure determination in NMR spectroscopy from geometrical restraints using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a semidefinite program (SDP). However, in practice there are often too few distance restraints for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between bond directions and axes of the principal-Axis-Frame. The optimization problem involving RDC is highly non-convex and requires good initializations. In this paper, we model the protein backbone as an articulated structure composed of rigid units. We estimate the rotation of each rigid unit using SDP relaxation that incorporates quaternion algebra. The two SDP based methods we propose - RDC-SDP and RDC-NOE-SDP have polynomial time complexity in the number of amino-acids, with average running time being 25 seconds and 3 minutes respectively for calculating protein fragments of typical size on a personal laptop. We further introduce the Cramer-Rao bound (CRB) to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy RDC measurements. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise, for realistic noise magnitude our SDP attains the CRB. Finally, we apply our proposed method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental distance restraints and RDC measurements obtained in two alignment medium. Comparing to the X-ray structure, the ubiquitin fragments considered are determined to 0.6 \AA\ resolution and the full protein structure formed from the fragments has 1 \AA\ error.
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determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods application to the determination of interdomain orientation in multidomain proteins
Journal of Magnetic Resonance, 2001Co-Authors: Ranajeet Ghose, David Fushman, David CowburnAbstract:In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal Axis Frame of the diffusion tensor to the molecular Frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor Frame to the molecular Frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.
G. Rosensteel - One of the best experts on this subject based on the ideXlab platform.
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Solutions to a time-dependent su(3) mean field Hamiltonian
Journal of Physics A: Mathematical and General, 2004Co-Authors: G. RosensteelAbstract:The time-dependent su(3) mean field equations are solved for a particular energy function relevant to nuclear structure. The model energy in the su(3) enveloping algebra is the sum of two terms which are the squared length of the angular momentum vector and the cubic rotational scalar X3 = tr(lql). The mean field solutions for this energy have constant intrinsic quadrupole moments q. In the three-dimensional space of all angular momentum components in the rotating principal Axis Frame, a trajectory is defined by the intersection of a sphere and a hyperboloid. This conclusion is similar to the classical rigid rotor for which a solution is the intersection of a sphere and the inertia ellipsoid.
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SU(3) mean field Hamiltonian
Journal of Physics A: Mathematical and General, 2002Co-Authors: G. Rosensteel, Ts DankovaAbstract:The su(3) mean field approximation describes collective nuclear rotation in a density matrix formalism. The densities ρ = q-i l/2 are 3×3 Hermitian matrices in the su(3) dual space, where q is the expectation of the quadrupole moment and l is the expectation of the angular momentum. The mean field approximation restricts these densities to a level surface of the su(3) Casimirs. Each level surface is a coadjoint orbit of the canonical transformation group SU(3). For each density ρ, the su(3) mean field Hamiltonian h[ρ] is an element of the su(3) Lie algebra. A model su(3) energy functional and the symplectic structure on the coadjoint orbit determine uniquely the su(3) mean field Hamiltonian. The densities in time-dependent su(3) mean field theory obey the dynamical equation i = [h[ρ],ρ] on a coadjoint orbit. The cranked mean field Hamiltonian is hΩ = h + i Ω, where Ω is the angular velocity of the rotating principal Axis Frame. A rotating equilibrium density in the body-fixed Frame is a self-consistent solution to the equation [hΩ[],] = 0.
Ranajeet Ghose - One of the best experts on this subject based on the ideXlab platform.
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determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods application to the determination of interdomain orientation in multidomain proteins
Journal of Magnetic Resonance, 2001Co-Authors: Ranajeet Ghose, David Fushman, David CowburnAbstract:In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal Axis Frame of the diffusion tensor to the molecular Frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor Frame to the molecular Frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.