Standard Normal Mode Analysis Research Articles

The effects of energy transfer and Hall currents on the instability of a viscous liquid sheet saturated in porous medium

Temporal instability theory is employed in the current study to examine the growth of anti-symmetric disturbances of a moving viscous fluid sheet embedded between two identical streaming perfect gas media. For simplicity, a two-dimensional model is offered without losing its generalization. A strong magnetic field (MF) is acted upon along with the normal direction of the plane of the model. The instability of a planar interface involving three liquids in permeable media yields major significance in geophysics and biomechanical. The novelty of this study is the thorough incorporation of many physical processes and approaches to examine the stability of liquid sheets in porous media. This investigation focuses on the impact of Hall currents and thermal effects. The findings of this study have significance for both basic comprehension and applications in practice. The contribution of the energy transmitted in the buoyancy condition, including the surface tension (ST), and restriction, is also reflected. The standard normal mode analysis is applied to achieve linear fundamental equations and the applicable boundary conditions (BCs). Therefore, the distributions of velocity, pressure, and temperature are calculated. The dimensionless examination reveals selected physical numerals. The impacts of these numerous physical features of the stability diagrams are established.

Linear analysis and head-on collision of dust ion-acoustic shock waves in un-magnetized electronegative collisional plasmas

The linear properties and head-on collision of dust ion-acoustic shock waves (DIASWs) are investigated in un-magnetized electronegative collisional plasmas comprising non-inertial thermal electron and light negative ion, inertial positive ion, and stationary dust grain with negative charges. In this regard, the dispersion relation is derived using the standard normal mode analysis and the two-sided damped Korteweg–deVries (dKdV) equations are derived employing the extended Poincaré Lighthill Kuo (ePLK) method. The effects of physical parameters on linear dispersion relation, formation of shocks, phase shift due to head-on collision, and collision process are studied. It is found that the effect of is more dominant to the wave frequency than that of and in a certain range of the group velocity of the DIASWs is increasing and then decreasing for the effect of the ratio of negative ion to electron density. The amplitude and width of the DIASWs increase with the enhancement of electron temperature and the ion-neutral collision plays a significant role in the formation of shock. The consequence of () the phase shift is increasing (decreasing). The results of this study may be useful to the investigation of space and astrophysical environment where the electronegative collisional plasma exists.

Dynamics of flow-induced instability in gyrogravitating complex viscoelastic quantum fluids

The flow-induced excitation dynamics of electrostatic dust-streaming instability mode supported in illimitable complex gyrogravitating viscoelastic quantum plasma fluids in a spatially flat-geometry configuration is analyzed in the non-relativistic regime. The constitutive lighter electrons (larger de-Broglie wavelength) are only treated as quantum degenerate particles leaving the rest as classical. The semi-analytic formalism is based on the fabric of generalized quantum hydrodynamic model ameliorated with a dimensionality-dependent gradient correction prefactor in the electronic quantum Bohm potential. The nonlinear logatropic barotropic effects arising from fluid turbulence is included. It assumes that perturbations in the longitudinal direction do not excite any transverse mode counterparts. A standard normal mode analysis yields a linear generalized (quartic) dispersion relation. A numerical illustrative perspective is executed in the extreme hydro-kinetic regimes. Active agencies affecting the fluid stability are identified and discussed. It is seen that the quantum parameter plays a destabilizing role in both the hydro-kinetic regimes. The equilibrium dust drift acts as a stabilizing agent in both the regimes. The quantum correction prefactor introduces stabilizing and destabilizing effects in the hydro-kinetic regimes; respectively. In addition, the Coriolis rotation introduces stabilizing effect in both the regimes. Finally, implications and applications of our results in the context of gyrogravitational compact dwarf stars and their environs in are summarily outlined.

Critical interpretation of CH- and OH- stretching regions for infrared spectra of methanol clusters (CH₃OH)n (n = 2-5) using self-consistent-charge density functional tight-binding molecular dynamics simulations.

Vibrational infrared (IR) spectra of gas-phase O-H⋅⋅⋅O methanol clusters up to pentamer are simulated using self-consistent-charge density functional tight-binding method using two distinct methodologies: standard normal mode analysis and Fourier transform of the dipole time-correlation function. The twofold simulations aim at the direct critical assignment of the C-H stretching region of the recently recorded experimental spectra [H.-L. Han, C. Camacho, H. A. Witek, and Y.-P. Lee, J. Chem. Phys. 134, 144309 (2011)]. Both approaches confirm the previous assignment (ibid.) of the C-H stretching bands based on the B3LYP/ANO1 harmonic frequencies, showing that ν3, ν9, and ν2 C-H stretching modes of the proton-accepting (PA) and proton-donating (PD) methanol monomers experience only small splittings upon the cluster formation. This finding is in sharp discord with the assignment based on anharmonic B3LYP/VPT2/ANO1 vibrational frequencies (ibid.), suggesting that some procedural faults, likely related to the breakdown of the perturbational vibrational treatment, led the anharmonic calculations astray. The IR spectra based on the Fourier transform of the dipole time-correlation function include new, previously unaccounted for physical factors such as non-zero temperature of the system and large amplitude motions of the clusters. The elevation of temperature results in a considerable non-homogeneous broadening of the observed IR signals, while the presence of large-amplitude motions (methyl group rotations and PA-PD flipping), somewhat surprisingly, does not introduce any new features in the spectrum.

Vibrational Analysis of an Ice Ih Model from 0 to 4000 cm–1 Using the Ab Initio WHBB Potential Energy Surface

We present an analysis of the vibrational modes of a model of hexagonal ice, ice Ih, comprised of 192 monomers with a core region of 105 monomers, using the ab initio WHBB potential energy surface [Wang, Y.; Shepler, B.; Braams, B.; Bowman, J. M. J. Chem. Phys. 2011, 134, 094509]. A standard normal-mode analysis and a local-monomer normal-mode analysis of 105 core monomers are performed to obtain harmonic frequencies and state densities of the "pseudo-translation" (0-400 cm(-1)), "libration" (500-1100 cm(-1)), monomer bend fundamental (~1600 cm), and O-H stretch (~3000-3700 cm(-1)) bands. In addition, the coupled local-monomer model is used to obtain the vibrational density of states in the bend fundamental and O-H stretch regions. The harmonic and local-monomer vibrational density of states obtained from core monomers are in good agreement with those of inelastic neutron scattering spectra, especially the latter, which accounts for anharmonic coupling of monomer modes. Full deuteration is also considered, and the vibrational density of states is again compared to experiment, where good agreement is found.

Instability of mixed convection in a vertical porous channel with uniform wall heat flux

Mixed convection in a vertical plane channel filled with a saturated porous medium is investigated. The boundary planes are considered as subject to symmetric uniform heat fluxes, resulting into a net fluid heating or cooling. Either upflow or downflow conditions are considered, thus exhibiting two distinct regimes: buoyancy-assisted and buoyancy-opposed. A basic stationary and parallel flow directed vertically along the channel is examined. The linear stability of this basic solution is developed through the standard normal-mode analysis. The solution of the eigenvalue problem for neutral stability is carried out numerically for the general oblique modes. An analytical solution is provided for the longitudinal modes, with a horizontal wave vector having a direction parallel to the boundary planes. An asymptotic analytical solution is also allowed for oblique modes with either a vanishingly small Péclet number or a vanishingly small wave number. The longitudinal modes are the most unstable, displaying their parametric domain of instability under buoyancy-opposed regime. In this regime, the longitudinal modes with sufficiently small wave numbers are always unstable. This conclusion suggests that conditions of flow reversal or crossing of parametric singularities, characteristic of the parallel flow solution under buoyancy-opposed regime, are unlikely to be observed in an experiment.

Arbitrary Amplitude Ion Acoustic Solitary Waves in An Unmagnetized Two Electron Population Ultra-Relativistic Dense Plasmas

The nonlinear wave structure of arbitrary amplitude ion acoustic solitary waves (IASWs) are studied in the Sagdeev’s pseudopotential framework for an ultra-relativistic degenerate dense plasma comprising cold and hot electrons and inertial ultra-cold ions. By employing standard normal-mode analysis the dispersion relation for linear waves is studied. The numerical results are presented to understand the features of ion acoustic solitary wave structures. It is shown that the present plasma model supports IASWs having positive potential well. Also, it is found that the small amplitude rarefactive double layer solution can exist in such a plasma system in some parametric region. It is shown that solitary structures and double layers are affected by relevant plasma parameters.

Stability of barotropic geostrophic flows revisited with some applications

The stability of inertial barotropic flows with a negative derivative of potential vorticity with respect to the stream function is investigated. A method developed by Pedlosky is extended to the above case and compared with classical results by Arnold. If such derivative is a constant, the stability criterion is valid also in the nonlinear regime. On the other hand, in the linear framework the obtained result is included in the criterion obtained by the standard normal mode analysis. Some applications to the East-West symmetry of the flow as well to the circulation over topography are considered.

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

We derive the normal modes for a rotating Coulomb ion crystal in a Penning trap, quantize the motional degrees of freedom, and illustrate how they can be driven by a spin-dependent optical dipole force to create a quantum spin simulator on a triangular lattice with hundreds of spins. The analysis for the axial modes (oscillations perpendicular to the two-dimensional crystal plane) follow a standard normal-mode analysis, while the remaining planar modes are more complicated to analyze because they have velocity-dependent forces in the rotating frame. After quantizing the normal modes into phonons, we illustrate some of the different spin-spin interactions that can be generated by entangling the motional degrees of freedom with the spin degrees of freedom via a spin-dependent optical dipole force. In addition to the well-known power-law dependence of the spin-spin interactions when driving the axial modes blue of the phonon band, we notice certain parameter regimes in which the level of frustration between the spins can be engineered by driving the axial or planar phonon modes at different frequencies. These systems may allow for the analog simulation of quantum spin glasses with large numbers of spins.

Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

Normal mode analysis (NMA) was introduced in 1930s as a framework to understand the structure of the observed vibration-rotation spectrum of several small molecules. During the past three decades NMA has also become a popular alternative to figuring out the large-scale motion of proteins and other macromolecules. However, the “standard” NMA is based on approximations, which sometimes are unphysical. Especially problematic is the assumption that atoms move only “infinitesimally”, which, of course, is an oxymoron when large amplitude motions are concerned. The “infinitesimal” approximation has the further unfortunate side effect of masking the physical importance of the coupling between vibrational and rotational degrees of freedom. Here, we present a novel formulation of the NMA, which is applied for finite motions in non-Eckart body-frame. Contrary to standard normal mode theory, our approach starts by assuming a harmonic potential in generalized coordinates, and tries to avoid the linearization of the coordinates. It also takes explicitly into account the Coriolis terms, which couple vibrations and rotations, and the terms involving Christoffel symbols, which are ignored by default in the standard NMA. We also computationally explore the effect of various terms to the solutions of the NMA equation of motions.

Fast and accurate computation schemes for evaluating vibrational entropy of proteins

Standard normal mode analysis (NMA) method is able to calculate vibrational entropy of proteins, but it is computationally intensive, especially for large proteins. To evaluate vibrational entropy efficiently and accurately, we, here, propose computation schemes based on coarse-grained NMA methods. This can be achieved by rescaling coarse-grained results with a specific factor that is derived on the basis of the linear correlation of protein vibrational entropy between standard NMA and coarse-grained NMA. Our coarse-grained NMA computation schemes can repeat correctly and efficiently the results of standard NMA for large proteins.

Ion acoustic solitary waves and double layers with nonextensive electrons and thermal positrons

By using Sagdeev’s pseudopotential technique, the problem of arbitrary amplitude ion acoustic solitary waves (IASWs) is discussed for a plasma comprising nonextensive electrons and thermal positrons. The standard normal-mode analysis is used to study the dispersion relation for linear waves. It is found that the present plasma model supports IASWs having positive as well as negative potential well. The influence of nonextensive electrons on the present plasma model is investigated for the existence of solitary waves. The investigation shows that the solitary structure ceases to exist when the parameter q crosses a certain limit. It is also found that both the small amplitude compressive and rarefactive double layer solution can exist in such a plasma system in some parametric region. It is shown that solitary structures and double layers are affected by nonextensivity, as well as by relevant plasma parameters.

Electron acoustic solitary waves and double layers with superthermal hot electrons

The problem of arbitrary amplitude electron acoustic solitary waves (EASWs) are discussed using Sagdeev’s pseudopotential technique for a plasma comprising cold electrons, superthermal hot electrons, and stationary ions. The standard normal-mode analysis is used to study the dispersion relation for linear waves. It is found that the present plasma model supports EASWs having negative potential. The influence of superthermal hot electrons on the present plasma model is investigated for the existence of solitary waves. The investigation shows that the solitary structure ceases to exist when the parameter κ crosses a certain limit. It is also found that the small amplitude double layer solution can exist in such a plasma system in some parametric regions. It is shown that solitary structures and double layers are affected by superthermality, as well as by relevant plasma parameters.

Anharmonic Normal Mode Analysis of Elastic Network Model Improves the Modeling of Atomic Fluctuations in Protein Crystal Structures

Protein conformational dynamics, despite its significant anharmonicity, has been widely explored by normal mode analysis (NMA) based on atomic or coarse-grained potential functions. To account for the anharmonic aspects of protein dynamics, this study proposes, and has performed, an anharmonic NMA (ANMA) based on the Cα-only elastic network models, which assume elastic interactions between pairs of residues whose Cα atoms or heavy atoms are within a cutoff distance. The key step of ANMA is to sample an anharmonic potential function along the directions of eigenvectors of the lowest normal modes to determine the mean-squared fluctuations along these directions. ANMA was evaluated based on the modeling of anisotropic displacement parameters (ADPs) from a list of 83 high-resolution protein crystal structures. Significant improvement was found in the modeling of ADPs by ANMA compared with standard NMA. Further improvement in the modeling of ADPs is attained if the interactions between a protein and its crystalline environment are taken into account. In addition, this study has determined the optimal cutoff distances for ADP modeling based on elastic network models, and these agree well with the peaks of the statistical distributions of distances between Cα atoms or heavy atoms derived from a large set of protein crystal structures.

Vibrational Raman Spectra from the Self-Consistent Charge Density Functional Tight Binding Method via Classical Time-Correlation Functions

The Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) method has been extended for the calculation of vibrational Raman spectra employing the Fourier Transform of Time-Correlation Function (FTTCF) formalism. As Witek and co-workers have already shown for a set of various organic molecules, the minimal basis SCC-DFTB approach performs surprisingly good in terms of polarizability calculations. Therefore, we were encouraged to use this electronic structure method for the purpose of Raman spectra calculations via FTTCF. The molecular polarizability was accessed via second order numeric derivatives of the SCC-DFTB energy with respect to the components of an external electric field “on-the-fly” during a molecular dynamics (MD) simulation. The finite electric field approach delivers Raman spectra that are in overall good agreement for most of 10 small organic model compounds examined in the gas phase compared to a standard Normal Mode Analysis (NMA) approach at the same (SCC-DFTB) and at a higher level of theory (BLYP aug-cc-pVTZ). With the use of reparametrized SCC-DFTB repulsive potentials, a distinct improvement of the Raman spectra from the SCC-DFTB/FTTCF protocol of conjugated hydrocarbons has been observed. Further QM/MM test calculations of l-phenylalanine in aqueous solution revealed larger deviations concerning vibrational frequencies and relative intensities for several stretching and bending modes in the benzene ring as compared to experimental results. Our SCC-DFTB/FTTCF approach was also tested against a hybrid method, in which polarizability calculations at the B3YLP 6-31G(d) level were performed on a trajectory at the SCC-DFTB level. We found that our SCC-DFTB/FTTCF protocol is not only much more efficient but in terms of the resulting Raman spectra also of similar accuracy compared to the hybrid approach. In our opinion, the more accurately calculated polarizabilities at the B3YLP 6-31G(d) level cannot compensate for the usually insufficient sampling of phase space when employing high level QM methods in a FTTCF framework.

Shape-dependent global deformation modes of large protein structures

Conformational changes are central to the functioning of pore-forming proteins that open and close their molecular gates in response to external stimuli such as pH, ionic strength, membrane voltage or ligand binding. Normal mode analysis (NMA) is used to identify and characterize the slowest motions in the gA, KcsA, ClC-ec1, LacY and LeuT Aa proteins at the onset of gating. Global deformation modes of the essentially cylindrical gA, KcsA, LacY and LeuT Aa biomolecules are reminiscent of global twisting, transverse and longitudinal motions in a homogeneous elastic rod. The ClC-ec1 protein executes a splaying motion in the plane perpendicular to the lipid bilayer. These global collective deformations are determined by protein shape. New methods, all-atom Monte Carlo Normal Mode Following and its simplification using a rotation–translation of protein blocks (RTB), are described and applied to gain insight into the nature of gating transitions in gA and KcsA. These studies demonstrate the severe limitations of standard NMA in characterizing the structural rearrangements associated with gating transitions. Comparison of all-atom and RTB transition pathways in gA clearly illustrates the impact of the rigid protein block approximation and the need to include all degrees of freedom and their relaxation in computational studies of protein gating. The effects of atomic level structure, pH, hydrogen bonding and charged residues on the large-scale conformational changes associated with gating transitions are discussed.

Consensus modes, a robust description of protein collective motions from multiple-minima normal mode analysis—application to the HIV-1 protease

Protein flexibility is essential for enzymatic function, ligand binding, and protein-protein or protein-nucleic acid interactions. Normal mode analysis has increasingly been shown to be well suited for studying such flexibility, as it can be used to identify favorable structural deformations that correspond to functional motions. However, normal modes are strictly relevant to a single structure, reflecting a particular minimum on a complex energy surface, and are thus susceptible to artifacts. We describe a new theoretical framework for determining "consensus" normal modes from a set of related structures, such as those issuing from a short molecular dynamics simulation. This approach is more robust than standard normal mode analysis, and provides higher collectivity and symmetry properties. In an application to HIV-1 protease, the low-frequency consensus modes describe biologically relevant motions including flap opening and closing that can be used in interpreting structural changes accompanying the binding of widely differing inhibitors.

Soliton energy of the Kadomtsev–Petviashvili equation in warm dusty plasma with variable dust charge, two-temperature ions, and nonthermal electrons

The propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ions, and nonthermal electrons is studied. By using the reductive perturbation theory, the Kadomtsev–Petviashivili (KP) equation is derived. The energy of the soliton has been calculated. By using standard normal modes analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the energy of the soliton and the angular frequency of the linear wave are also discussed. It is shown that the amplitude of solitary waves of the KP equation diverges at the critical values of plasma parameters. We derive solitons of a modified KP equation with finite amplitude in this situation.

Comparative study of various normal mode analysis techniques based on partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine-stretch, the spectrum of quinine and a bis-cinchona derivative, and the low frequency modes of the LAO binding protein.

Ion acoustic solitary waves in plasma with nonthermal electron, positron and warm ion

In this paper, the characteristics of ion acoustic solitary waves are studied in plasmas containing warm ion fluid, non-thermally distributed electron and positron. We study the effects of non-thermal electrons and ion temperature on solitons by Pseudo-potential method and show that the parametric region where ion acoustic solitons can exist is modified. We also obtain linear dispersion relation by using the standard normal-modes analysis.