Structure Of Normal Modes Research Articles

Influence of the magnetic field and the mean flow configuration on spatial structure and growth rate of normal modes

The first part of the work presents the results of numerical experiments with the magnetohydrodynamic model of “shallow water” to assess the degree of influence of the magnetic field on the development of instabilities conditioned by a combination of inhomogeneities in the mean flow and the mean magnetic field. Normal mode calculations have confirmed the earlier obtained result on the different influence of weak and strong magnetic fields on the instability of differential rotation. Calculations have shown that a weak magnetic field stabilizes the development of instabilities, whereas a strong magnetic field, on the contrary, enhances the instability. Azimuthal inhomogeneities of differential rotation in all cases contribute to the development of instabilities. In the second part of the work, we examine the spatial structure of normal modes and make an attempt to interpret the torsional oscillations observed in the atmospheres of Earth and the Sun. Calculations have shown that regular axisymmetric disturbances can be caused by the formation of a cyclonic vortex above the pole, which is characteristic of Earth's atmosphere and, possibly, of the Sun's atmosphere. The least damped normal mode of a stable polar cyclone has a structure of torsional oscillations. Flow anomalies and the development of an anticyclonic eddy in winter at midlatitudes destroy torsional oscillations and lead to a rapid amplification of normal modes, which are more complex in structure.

Влияние магнитного поля и конфигурации среднего течения на пространственную структуру и скорость роста нормальных мод

The first part of the work presents the results of numerical experiments with the magnetohydrodynamic model of “shallow water” to assess the degree of influence of the magnetic field on the development of instabilities conditioned by a combination of inhomogeneities in the mean flow and the mean magnetic field. Numerical simulation of normal modes has confirmed the earlier obtained result on the different influence of weak and strong magnetic fields on the instability of differential rotation. Calculations have shown that a weak magnetic field stabilizes the development of instabilities, whereas a strong magnetic field, on the contrary, enhances the instability. Azimuthal inhomogeneities of differential rotation in all cases contribute to the development of instabilities. In the second part of the work, we examine the spatial structure of normal modes and make an attempt to interpret the torsional oscillations observed in the atmospheres of Earth and the Sun. Calculations have shown that regular axisymmetric disturbances (torsional oscillations) can be caused by the formation of a cyclonic vortex above the pole, which is characteristic of Earth’s atmosphere and, possibly, of the Sun’s atmosphere. The least damped normal mode of a stable polar cyclone has a structure of torsional oscillations. Flow anomalies and the development of an anticyclonic eddy in winter at midlatitudes destroy torsional oscillations and lead to a rapid amplification of normal modes, which are more complex in structure.

Exploring the structure–property relationship of ethylenediammonium hydrogen phosphite: Insights from XRD, vibrational, DFT, and biological evaluation

The interaction between the molecules of phosphonic acid (H2P(H)O3) and ethylenediamine (NH2CH2CH2NH2) reacts in an aqueous solution and results in the formation of salt molecules with two NH∙∙∙O hydrogen bonds. The calculated stabilization energy of the 1:1 salt molecule, which represents the strength of the two NH∙∙∙O hydrogen bonds, is 8.063 kcal/mol (33.735 kJ/mol). The title compound crystallizes in the centrosymmetric space group Pbca of the orthorhombic system with eight molecules per unit cell. The three-dimensional supramolecular network is formed by hydrogen bonds between every hydrogen atom in both of the NH3+ groups of the ethylenediammonium cation. Hirshfeld surfaces and two-dimensional fingerprint plots were used to analyze the interactions of ethylenediammonium cations and hydrogen phosphite anions forming a three-dimensional supramolecular structure. Practically, two types of interactions, i.e. NH∙∙∙O and H∙∙∙H, are observed for both building units, ethylenediammonium cation and the hydrogen phosphite anion, which cover 100 % of the HS surface of each unit. Density functional theory (DFT) computations of normal mode force constants and structure optimizations were employed to evaluate the molecular structure, fundamental vibrational frequencies, and vibrational band intensities. The utilization of potential energy distribution (PED) allowed for the determination of comprehensive vibrational assignments for the wave numbers. The interactions involving the charge transfers of the supramolecular unit are explained by the computed HOMO and LUMO energy gap of 5.193 eV. To prove that the EDHP has stabilized, NBO analysis has been done. NBO studies establish that strong intra and intermolecular stabilization exists between the ethylenediammonium cation and the hydrogen phosphite anion. Furthermore, to investigate the synthetic chemical EDHP as a possible drug candidate, molecular docking studies and drug-likeness evaluation have been carried out. The best binding energy of the obtained cluster is −3.85 kcal/mol. The rmsd value is found to be 1.950 (≤2 Å) which is fairly good and confirms the best superimposed docked pose. Thus Molecular docking studies reveal that EDHP molecule has a substantial binding affinity for the SARS-CoV-2 protein and can serve as a promising drug candidate. The bioavailability score of 0.55 from pharmacokinetics study suggests that EDHP may have moderate bioavailability.

Properties of Magnetohydrodynamic Normal Modes in the Earth's Magnetosphere

AbstractThe Earth's magnetosphere supports a variety of Magnetohydrodynamic (MHD) normal modes with Ultra Low Frequencies (ULF) including standing Alfvén waves and cavity/waveguide modes. Their amplitudes and frequencies depend in part on the properties of the magnetosphere (size of cavity, wave speed distribution). In this work, we use ∼13 years of Time History of Events and Macroscale Interactions during Substorms satellite magnetic field observations, combined with linearized MHD numerical simulations, to examine the properties of MHD normal modes in the region L > 5 and for frequencies <80 mHz. We identify persistent normal mode structure in observed dawn sector power spectra with frequency‐dependent wave power peaks like those obtained from simulation ensemble averages, where the simulations assume different radial Alfvén speed profiles and magnetopause locations. We further show with both observations and simulations how frequency‐dependent wave power peaks at L > 5 depend on both the magnetopause location and the location of peaks in the radial Alfvén speed profile. Finally, we discuss how these results might be used to better model radiation belt electron dynamics related to ULF waves.

Modal structure of the sound field in a shallow-water waveguide with a gassy sediment layer: Experiment and theory

Motivated by a series of experiments in the Lake Kinneret (Israel), the paper investigates low-frequency sound propagation in the three-layer model of the shallow water waveguide, where a thin layer of gas-saturated sediment is situated between a homogeneous fluid sub-bottom and a continuously stratified water column. Typical values of the thickness and sound speed in the gassy layer are 1 m and 250 m/s. The layer is thin compared to typical water depth of about 40 m. Normal mode structure of the acoustic field is analyzed. It is shown that with increasing frequency each normal mode transforms into a mode trapped in the gassy layer. These modes have unusually small phase and group speeds that are significantly less than the sound speed in water. Theoretically predicted normal mode dispersion curves are compared to the dispersion curves retrieved from observations of shipping noise. Phase speeds of normal modes are measured by cross-correlatingthe noise recorded on two sparse vertical arrays. A technique is proposed for solving the inverse problem of determining the parameters of a gas-saturated layer by matching the measured and modeled frequency dependencies of the normal mode phase speed.

Domain-Based Protein Docking with Extremely Large Conformational Changes

Proteins are key components in many processes in living cells, and physical interactions with other proteins and nucleic acids often form key parts of their functions. In many cases, large flexibility of proteins as they interact is key to their function. To understand the mechanisms of these processes, it is necessary to consider the 3D structures of such protein complexes. When such structures are not yet experimentally determined, protein docking has long been present to computationally generate useful structure models. However, protein docking has long had the limitation that the consideration of flexibility is usually limited to very small movements or very small structures. Methods have been developed which handle minor flexibility via normal mode or other structure sampling, but new methods are required to model ordered proteins which undergo large-scale conformational changes to elucidate their function at the molecular level. Here, we present Flex-LZerD, a framework for docking such complexes. Via partial assembly multidomain docking and an iterative normal mode analysis admitting curvilinear motions, we demonstrate the ability to model the assembly of a variety of protein–protein and protein-nucleic acid complexes.

Spatial structure of unstable normal modes in a glass-forming liquid

The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.

The structure of normal modes in parallel ideal optical fibers with strong coupling

In this paper, we studied an effect of strong evanescent coupling on the structure of normal modes in a system of parallel ideal multimode optical fibers. Using the formalism of the degenerate perturbation theory and a scalar waveguide equation for this system, analytical expressions of higher-order supermodes and their propagation constants have been determined. We have shown that the structure of modes in the case of strong evanescent coupling coincides with the structure of normal modes for weakly coupled parallel fibers. We have demonstrated that in the presence of strong coupling, expressions for corrections to the scalar propagation constant are modified, deducing them analytically.

Soft regions of protein surface are potent for stable dimer formation

By having knowledge about the characteristics of protein interaction interfaces, we will be able to manipulate protein complexes for therapies. Dimer state is considered as the primary alphabet of the most proteins’ quaternary structure. The properties of binding interface between subunits and of noninterface region define the specificity and stability of the intended protein complex. Considering some topological properties and amino acids’ affinity for binding in interfaces of protein dimers, we construct the interface-specific recurrence plots. The data obtained from recurrence quantitative analysis, and accessibility-related metrics help us to classify the protein dimers into four distinct classes. Some mechanical properties of binding interfaces are computed for each predefined class of the dimers. The computed mechanical characteristics of binding patch region are compared with those of nonbinding region of proteins. Our observations indicate that the mechanical properties of protein binding sites have a decisive impact on determining the dimer stability. We introduce a new concept in analyzing protein structure by considering mechanical properties of protein structure. We conclude that the interface region between subunits of stable dimers is usually mechanically softer than the interface of unstable protein dimers.AbbreviationsAABaverage affinity for bindingANManisotropic network modelAPCaffinity propagation clusteringASAaccessible surface areaCCDinter residues distanceCSCcomplex stability codeDMdistance matrixΔGdissPISA-computed dissociation free energyGNMGaussian normal mode analysisNMAnormal mode analysisPBPprotein binding patchPISAproteins, interfaces, structures and assembliesrASArelative accessible area in respect to unfolded state of residuesRMrecurrence matrixrPrelative protrusionRPrecurrence plotRQArecurrence quantitative analysisSEMstandard error of meanCommunicated by Ramaswamy H. Sarma

Short Pulses of Normal Modes of Electromagnetically Induced Transparency

The process of propagation of short probe pulses of electromagnetically induced transparency has been analyzed theoretically in the case of elliptically polarized control radiation. As a model of a resonant medium, a Λ scheme of quantum transitions between the $$^{3}{{P}_{0}}$$ , $$^{3}P_{1}^{0}$$ , and $$^{3}{{P}_{2}}$$ degenerate levels of the 208Pb isotope has been used. The situation in which the probe radiation is rather weak compared to the control radiation has been examined. In this case, the field of the probe pulse can be represented as a sum of the fields of two elliptically polarized pulses that propagate in the medium independently of one another without changing their polarization state, which makes it possible to interpret them as nonstationary normal modes. Numerical simulation has shown that the structure of normal modes depends on the ratio of the width of the spectrum of the input probe pulse to the Doppler frequency broadening of the quantum transition that is resonant to the probe field. If this ratio is small, each mode in the medium is a single pulse similar to the input probe pulse. Under these conditions, the propagation of each normal mode in the medium can be fairly well characterized by the group velocity depending on the intensity and the state of polarization of the control radiation. As this ratio increases, normal modes in the medium initially acquire the shape of a regular decaying train of pulses, and then their structure becomes chaotic. The described evolution is accompanied by an increase in the energy absorption of the probe radiation by the medium and by a significant deterioration in the applicability of the notion of group velocity for describing the propagation process of normal modes.

Короткие импульсы нормальных мод электромагнитно индуцированной прозрачности

AbstractThe process of propagation of short probe pulses of electromagnetically induced transparency has been analyzed theoretically in the case of elliptically polarized control radiation. As a model of a resonant medium, a Λ scheme of quantum transitions between the $$^{3}{{P}_{0}}$$ , $$^{3}P_{1}^{0}$$ , and $$^{3}{{P}_{2}}$$ degenerate levels of the ^208Pb isotope has been used. The situation in which the probe radiation is rather weak compared to the control radiation has been examined. In this case, the field of the probe pulse can be represented as a sum of the fields of two elliptically polarized pulses that propagate in the medium independently of one another without changing their polarization state, which makes it possible to interpret them as nonstationary normal modes. Numerical simulation has shown that the structure of normal modes depends on the ratio of the width of the spectrum of the input probe pulse to the Doppler frequency broadening of the quantum transition that is resonant to the probe field. If this ratio is small, each mode in the medium is a single pulse similar to the input probe pulse. Under these conditions, the propagation of each normal mode in the medium can be fairly well characterized by the group velocity depending on the intensity and the state of polarization of the control radiation. As this ratio increases, normal modes in the medium initially acquire the shape of a regular decaying train of pulses, and then their structure becomes chaotic. The described evolution is accompanied by an increase in the energy absorption of the probe radiation by the medium and by a significant deterioration in the applicability of the notion of group velocity for describing the propagation process of normal modes.

The Effect of Fast Normal Mode Structure and Magnetopause Forcing on FLRs in a 3‐D Waveguide

AbstractThis paper investigates the excitation of waveguide modes in a nonuniform dipole equilibrium and, further, their coupling to field line resonances (FLRs). Waveguide modes are fast compressional ultralow frequency (ULF) waves, whose structure depends upon the magnetospheric equilibrium and the solar wind driving conditions. Using magnetohydrodynamic simulations, we consider how the structure of the excited waveguide mode is affected by various forms of magnetopause driving. We find that the waveguide supports a set of normal modes that are determined by the equilibrium. However, the particular normal modes that are excited are determined by the structure of the magnetopause driver. A full understanding of the spatial structure of the normal modes is required in order to predict where coupling to FLRs will occur. We show that symmetric pressure driving about the noon meridian can excite normal modes which remain around to drive resonances for longer than antisymmetric driving. Further, the critical quantity in terms of efficient coupling is the magnetic pressure gradient aligned with the resonance.

Effect of disorder on coherent quantum phase slips in Josephson junction chains

We study coherent quantum phase-slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes, which are all localized by the area disorder). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total QPS amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains.

Theory of coherent quantum phase slips in Josephson junction chains with periodic spatial modulations

We study coherent quantum phase-slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes). These, in turn, are affected by spatial inhomogeneities in the ring. We analyze the case of weak periodic modulations of the system parameters and calculate the corresponding modification of the quantum phase-slip amplitude.

Secular instabilities of Keplerian stellar discs

We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags which include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the m = 1 mode has positive pattern speed. Waterbags excluding circular orbits (bands) have two linear normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.

Interplay between isoscalar and isovector correlations in neutron-rich nuclei

The interplay between isoscalar and isovector correlations in the 1$^{-}$ states in neutron-rich (N$\neq$Z) even-even nuclei is studied, taking examples of the nuclei, $^{22}_{8}$O$_{14}$ and $^{24}_{8}$O$_{16}$. The excitation modes explored are isovector dipole and isoscalar compression dipole modes. The self-consistent Hartree-Fock plus the random-phase approximation with the Skyrme interaction, SLy4, is solved in coordinate space so as to take properly into account the continuum effect. The isovector peak induced by isoscalar correlation, the isoscalar peak induced by isovector correlation, and the possible collective states made by both isoscalar and isovector correlations, ("iS-iV pigmy resonance"), are shown. The strong neutron-proton interaction in nuclei can be responsible for controlling the isospin structure of normal modes. It is explicitly shown that in the scattering by isoscalar (isovector) particles on N$\neq$Z even-even nuclei isovector (isoscalar) strength in addition to isoscalar (isovector) strength may be populated.

Imaging Photon Lattice States by Scanning Defect Microscopy

Microwave photons inside lattices of coupled resonators and superconducting qubits can exhibit surprising matter-like behavior. Realizing such open-system quantum simulators presents an experimental challenge and requires new tools and measurement techniques. Here, we introduce Scanning Defect Microscopy as one such tool and illustrate its use in mapping the normal-mode structure of microwave photons inside a 49-site Kagome lattice of coplanar waveguide resonators. Scanning is accomplished by moving a probe equipped with a sapphire tip across the lattice. This locally perturbs resonator frequencies and induces shifts of the lattice resonance frequencies which we determine by measuring the transmission spectrum. From the magnitude of mode shifts we can reconstruct photon field amplitudes at each lattice site and thus create spatial images of the photon-lattice normal modes.

Elasticity of frictionless particles near jamming.

We study the linear elastic response of harmonic disk packings near jamming via three types of probes: (i) point forcing, (ii) constrained homogeneous deformation of subregions of large systems, and (iii) unconstrained deformation of the full system subject to periodic boundary conditions. For the point forcing, our results indicate that the transverse component of the response is governed by a lengthscale ξT, which scales with the confining pressure, p, as ξT∼p-0.25, while the longitudinal component is governed by ξL, which scales as ξL∼p-0.4. The former scaling is precisely the transverse lengthscale, which has been invoked to explain the structure of normal modes near the density of states anomaly in sphere packings, while the latter is much closer to the rigidity length, l*∼p-0.5, which has been invoked to describe the jamming scenario. For the case of constrained homogeneous deformation, we find that μ(R), the value of the shear modulus measured in boxes of size R, gives a value much higher than the continuum result for small boxes and recedes to its continuum limit only for boxes bigger than a characteristic length, which scales like p-0.5, precisely the same way as l*. Finally, for the case of unconstrained homogeneous deformation, we find displacement fields with power spectra, which are consistent with independent, uncorrelated Eshelby transformations. The transverse sector is amazingly invariant with respect to p and very similar to what is seen in Lennard-Jones glasses. The longitudinal piece, however, is sensitive to p. It develops a plateau at long wavelength, the start of which occurs at a length that grows in the p→0 limit. Strikingly, the same behavior is observed both for applied shear and dilation.

Observations and analysis of environment and acoustic field changed by the passage of typhoon Damrey in the Yellow Sea in 2012

In order to investigate the environment and acoustic filed change induced by typhoon in shallow sea, we conducted two experiments just before and after the passage of typhoon Damrey, which is the strongest to affect the area north of the Yangtze River since 1949, in the Yellow sea in 2012. The data show that the temperature of the whole water column increases dramatically except the sea surface layer after the passage of Damrey while the salinity decreases obviously. The thermocline deepens and weakens, which leads to a change of internal wave activity. The transmission losses (TL) of the two experiments show that the environment change induced by typhoon can increase the TL as large as 8 dB at a distance of 9.2 km and depth of 15 m. The scintillation index (SI) of the sound intensity is simulated to estimate the change of the effect of internal wave activity on acoustic field showing that the SI decreases to a half after the typhoon’s passage. The normal mode structures of the two experiments are also significantly different due to the thermocline changes. In addition, the signal arrives earlier after the typhoon’s passage due to the water temperature increase.

Horizontal coherence of sound propagation in the presence of internal waves on the New Jersey continental shelf

The knowledge of spatial coherence of sound field is required for sonar application and array design. In shallow water waveguides, the spatial and temporal evolution of the temperature field induced by internal waves will cause signal fluctuations and variations in spatial coherence. During the Shallow Water Acoustic Experiment 2006, the three dimensional temperature field of internal waves was measured and reconstructed while acoustic signals were simultaneously transmitted between various sources and an L-array. These internal wave events have been used to investigate the internal wave effect on temporal coherence and vertical structures of acoustic normal modes [Wan and Badiey, J. Acoust. Soc. Am. 135, 2014]. In this paper, the horizontal structures of acoustic normal modes are examined. The arrival angles of normal modes are analyzed. The horizontal coherence of sound field is obtained at different frequencies for these internal wave events. The relationship between horizontal coherence and internal wave parameters, such as propagation direction, speed, and amplitude, is discussed. [Work supported by ONR322OA.]