Natural modes of a coupled non-linear system

The natural modes of a non-linear system with two degrees of freedom are investigated. The system, which may contain either hard or soft springs, is shown to possess three modes of vibration one of which does not have any counterpart in the linear theory. The stability analysis indicates the existence of seven different modal stability patterns depending on the values of two parameters of non-linearity.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Computer modelling approach to study the modes of binding of alpha- and beta-anomers of D-galactose, D-fucose and D-glucose to L-arabinose-binding protein

The modes of binding of alpha- and beta-anomers of D-galactose, D-fucose and D-glucose to L-arabinose-binding protein (ABP) have been studied by energy minimization using the low resolution (2.4 A) X-ray data of the protein. These studies suggest that these sugars preferentially bind in the alpha-form to ABP, unlike L-arabinose where both alpha- and beta-anomers bind almost equally. The best modes of binding of alpha- and beta-anomers of D-galactose and D-fucose differ slightly in the nature of the possible hydrogen bonds with the protein. The residues Arg 151 and Asn 232 of ABP from bidentate hydrogen bonds with both L-arabinose and D-galactose, but not with D-fucose or D-glucose. However in the case of L-arabinose, Arg 151 forms hydrogen bonds with the hydroxyl group at the C-4 atom and the ring oxygen, whereas in case of D-galactose it forms bonds with the hydroxyl groups at the C-4 and C-6 atoms of the pyranose ring. The calculated conformational energies also predict that D-galactose is a better inhibitor than D-fucose and D-glucose, in agreement with kinetic studies. The weak inhibitor D-glucose binds preferentially to one domain of ABP leading to the formation of a weaker complex. Thus these studies provide information about the most probable binding modes of these sugars and also provide a theoretical explanation for the observed differences in their binding affinities.

Coupled ocean-atmosphere inter-decadal modes in the tropics

Homogencous upper air data for 50 years (1949-1998) from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project, sea surface temperatures and sea level pressure are used to bring out the three dimensional structure of two dominant decadal/multi-decadal variations in the tropics. The global three dimensional modes represent generalized forms of inter-decadal modes studied earlier only with surface data. In the vertical, both modes show approximate first baroclinic structures over the tropics. The Walker circulation associated with the multidecadal mode has a wavenumber two structure in the zonal direction. It is shown that the magnitude of major ascending and descending motions associated with the multi-decadal Hadley and Walker circulations, are comparable to those associated with the dominant inter-annual mode. Implications of these large scale global circulations associated with the low frequency oscillations in modulating regional climate on a inter-annual time scale are discussed.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventionalsimulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter. [DOI:10.1115/1.4001904]

Correlations between frequency of infra-red active vibrational modes and copper-oxygen distance in copper oxides. Application to superconductors

The infra-red spectra of a large number of ternary Cu(II) oxides with at least a quasi square-planar coordination of oxygen around the copper ions have been studied. The frequency of the bands with the highest frequency,v max, is found to correlate extremely well with the shortest Cu–O distance.v max increases at an impressive rate of sim20 cm–1 per 0.01 Å when the Cu–O distance becomes less than 1.97 Å, which is the Cu2+–O2– distance in square-planar CuO4 complexes as obtained from empirical ionic radii considerations. The marked sensitivity may be used as a ldquotitrationrdquo procedure not only to assign bands but also to obtain diagnostic information about local coordination in compounds derived, for example, from the YBa2Cu3O7–d structure such as LaCaBaCu3O7–d . The only example where this correlation fails is in the two-layer non-superconducting oxides derived from La2(Ca, Sr)Cu2O6. The significance of this result is discussed. The marked dependence of frequency on the bond-distance is qualitatively examined in terms of an increased electron-phonon coupling to account for the observed tendency of the superconducting transition temperature to go through a maximum as the average basal plane Cu–O distance is decreased.

Modes of binding of guanosine monophosphates to ribonuclease T1 - A computer modelling study

Computer-modelling studies on the modes of binding of the three guanosine monophosphate inhibitors 2'-GMP, 3'-GMP, and 5'-GMP to ribonuclease (RNase) T1 have been carried out by energy minimization in Cartesian-coordinate space. The inhibitory power was found to decrease in the order 2'-GMP > 3'-GMP > 5'-GMP in agreement with the experimental observations. The ribose moiety was found to form hydrogen bonds with the protein in all the enzyme-inhibitor complexes, indicating that it contributes to the binding energy and does not merely act as a spacer between the base and the phosphate moieties as suggested earlier. 2'-GMP and 5'-GMP bind to RNase T1 in either of the two ribose puckered forms (with C3'-endo more favoured over the C2'-endo) and 3'-GMP binds to RNase T1 predominantly in C3'-endo form. The catalytically important residue His-92 was found to form hydrogen bond with the phosphate moiety in all the enzyme-inhibitor complexes, indicating that this residue may serve as a general acid group during catalysis. Such an interaction was not found in either X-ray or two-dimensional NMR studies.

Solvation dynamics in liquid water. A novel interplay between librational and diffusive modes

A microscopic calculation of the solvation dynamics of an ion in liquid water is presented. The calculated solvation time correlation function shows an ultrafast Gaussian decay which carries about 70%–90% of the strength followed by a biexponential decay with time constants equal to 250 fs and 1 ps. These results are in excellent agreement with the computer simulations of Maroncelli and Fleming and also with the experimental findings of Barbara and Jarzeba. In addition, we find that both the rotational librations and the intermolecular translational vibrational modes of water contribute significantly to the initial Gaussian decay.

Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics

Modes of binding of 2'-AMP to RNase T1. A computer modeling study

The modes of binding of adenosine 2'-monophosphate (2'-AMP) to the enzyme ribonuclease (RNase) T1 were determined by computer modelling studies. The phosphate moiety of 2'-AMP binds at the primary phosphate binding site. However, adenine can occupy two distinct sites--(1) The primary base binding site where the guanine of 2'-GMP binds and (2) The subsite close to the N1 subsite for the base on the 3'-side of guanine in a guanyl dinucleotide. The minimum energy conformers corresponding to the two modes of binding of 2'-AMP to RNase T1 were found to be of nearly the same energy implying that in solution 2'-AMP binds to the enzyme in both modes. The conformation of the inhibitor and the predicted hydrogen bonding scheme for the RNase T1-2'-AMP complex in the second binding mode (S) agrees well with the reported x-ray crystallographic study. The existence of the first mode of binding explains the experimental observations that RNase T1 catalyses the hydrolysis of phosphodiester bonds adjacent to adenosine at high enzyme concentrations. A comparison of the interactions of 2'-AMP and 2'-GMP with RNase T1 reveals that Glu58 and Asn98 at the phosphate binding site and Glu46 at the base binding site preferentially stabilise the enzyme-2'-GMP complex.

Modes of binding of α(1–2) linked manno-oligosaccharides to concanavalin A

Three-dimensional structures of the complexes of concanavalin A (ConA) with alpha(1-2) linked mannobiose, triose and tetraose have been generated with the X-ray crystal structure data on native ConA using the CCEM (contact criteria and energy minimization) method. All the constituting mannose residues of the oligosaccharide can reach the primary binding site of ConA (where methyl-alpha-D-mannopyranose binds). However, in all the energetically favoured complexes, either the non-reducing end or middle mannose residues of the oligosaccharide occupy the primary binding site. The middle mannose residues have marginally higher preference over the non-reducing end residue. The sugar binding site of ConA is extended and accommodates at least three alpha(1-2) linked mannose residues. Based on the present calculations two mechanisms have been proposed for the binding of alpha(1-2) linked mannotriose and tetraose to ConA.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.