A theoretical model for the collective motion of proteins by means of principal component analysis

A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the C _a atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0.2–0.4 ps and slow relaxation time of long diffusion about 1–2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from −0.746 to −0.938 for the real part and from −0.528 to −0.665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.     

Application of the SCC method to the multi-O(4) model: The collective Hamiltonian

The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate(SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov(TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the sp...     

Method for identification of the nuclear collective modes

The analysing power measurements for inelastic scattering of polarized protons with excitation of the first 2⁺ level provide a sensitive method to distinguish two simple collective models-axially symmetric rotational and vibrational. The method is illustrated by the measurements of 24.5 MeV protons scattering on ^148,152Sm and some coupled channel calculations.     

A numerical test of the collective coordinate method

The purpose of this Letter is to compare the dynamics of the kink interacting with the imperfection which follows from the collective coordinate method with the numerical results obtained on the ground of the field theoretical model. We showed that for weekly interacting kinks the collective coordinate method works similarly well for low and extremely large speeds.     

On the description of dissipative collective motion

We use a recently developed time-dependent projection method to describe the dissipation of collective motion coupled to an intrinsic system. The underlying physical picture is similar to that of the linear response approach. Our approach is, however, different from the conceptual point of view. We do not resort to a quasistatic picture but use instead a time-dependent projector. Furthermore, we project on a model space which includes the intrinsic hamiltonian in addition to the collective subspace. In this way we obtain a Fokker-Planck equation for the collective variables which is coupled to a transport equation describing the evolution of the temperature of the intrinsic system.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; anharmonic coupling terms render the collective potential to be velocity-dependent.     

The scattering of quantized solitons in the non-linear Schrödinger theory

The scattering of quantized solitons in non-linear Schrödinger theory is treated using the collective coordinate method of Gervais, Jevicki and Sakita. The phase shift for soliton-soliton scattering is calculated up to the one-loop level. We find that the quantum correction vanishes. This result coincides in the first two terms of an expansion in $\text{h}\text{?}$ with the exact amplitude calculated from a quantum mechanical N-body problem.     

Dynamic collective displacements of atoms in metals and their role in the vacancy mechanism of diffusion

The phenomenon of dynamic collective displacements of atoms in face-centered cubic crystals has been revealed using molecular dynamics method. This phenomenon plays an important role in the vacancy mechanism of diffusion. The vacancy mechanism is provided by the collision of two regions of collective atomic displacements that move a migrating atom and a vacancy toward each other. The collective thermal atomic displacements from crystal lattice sites occur as a result of the nonuniform momentum distribution of atoms according to the Maxwellian distribution. Owing to their statistical nature, the degree of correlation of the atomic displacements depends neither on the temperature nor on the interatomic interaction potential.     

Flow effects on jet energy loss with detailed balance

In the presence of collective flow a new model potential describing the interaction of the hard jet with scattering centers is derived based on the static color-screened Yukawa potential.The flow effect on jet quenching with detailed balance is investigated in pQCD.It turns out,considering the collective flow with velocity vzalong the jet direction,the collective flow decreases the LPM destructive interference comparing to that in the static medium.The gluon absorption plays a more important role in the moving medium.The collective flow increases the energy gain from gluon absorption,however,decreases the energy loss from gluon radiation,which is(1-vz)times as that in the static medium to the first order of opacity.In the presence of collective flow,the second order in opacity correction is relatively small compared to the first order.So that the total effective energy loss is decreased.The flow dependence of the energy loss will affect the suppression of high pThadron spectrum and anisotropy parameter v2in high-energy heavy-ion collisions.     

Microscopic descriptions of collective SD bands in the A=190 mass region with the Gogny force

In the framework of microscopic models, we present two methods for describing superdeformed (SD) band properties. The first one is the cranked Hartree-Fock-Bogoliubov (HFB) method, without and with inclusion of particle number projection. The second one is the Gaussian overlap approximation to the generator coordinate method (GCM+GOA) with whichwetreat the five quadrupole collective coordinates. Both methods use the Gogny force. Moments of inertia and excitation energies of SD bands are calculated and compared with experimental results.     

Band diagram of spin waves in a two-dimensional magnonic crystal

The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks. We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimensional effective wave vector that characterizes each mode in this magnonic metamaterial.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson. II

The generator coordinate method is used to relate the interacting boson model of Arima and lachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; unharmonic coupling terms render the collective potential to be velocity dependent. The mapping of operators of the interacting boson model onto those of the Bohr-Mottelson model turns out to be of Holstein-Primakoff type.     

Boson description of nuclear collective motion. I

As the first part of the series on the application of the boson expansion method to the nuclear collective motion, the method of Kishimoto and Tamura is illustrated by taking a simple case of boson expansion up to second order. By taking into account the effect of particle channel by the projection technique, the lowest mode is shown to have the same property as the RPA phonon.     

Relationship between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model and the collective model through an isometric transformation. It associated complex parameters to the original boson operators whereas the ultimate collective variables are real. The mapping of operators of the interacting boson model onto those of the collective model turns out to be of Holstein-Primakoff type.     

Boson description of nuclear collective motion II. Application to octupole vibration

As the first part of the series on the application of the boson expansion method to the nuclear collective motion, the method of Kishimoto and Tamura is illustrated by taking a simple case of boson expansion up to second order. By taking into account the effect of particle channel by the projection technique, the lowest mode is shown to have the same property as the RPA phonon.