Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

Sorbate properties and cage-to-cage diffusion of argon in NaCaA: a molecular dynamics study

Detailed molecular dynamics simulations of argon in zeolite NaCaA are reported. Thermodynamic, structural, and dynamical properties of the sorbate as a function of temperature have been obtained. The properties calculated include various site-site radial distribution functions, different energy distribution functions, selfdiffusion coefficients, the power spectra, and properties relating to cage-to-cage diffusion. The results suggest that sorbate is delocalized above 300 K. Both modes of cage-to-cage diffusion-the surface-mediated and centralized diffusion-are associated with negative barrier heights. Surprisingly, rate of cage-to-cage diffusion is associated with negative and positive activation energies below and above 500 K. The observed differences in the behavior of the rate of cage-to-cage diffusion between Xe-NaY and Ar-NaCaA systems and the nature of the potential energy surface are discussed. Presence of sorbatezeolite interactions results in significant enhancement in the rate of cage-to-cage diffusion and rate of cage visits. It is shown that properties dependent on the long-time behavior such as the diffusion coefficient and the rate of cages visited exhibit the expected Arrhenius dependence on temperature.

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations. (C) 2011 American Institute of Physics. doi:10.1063/1.3516588]

Friction-formed liquid droplets

The formation of nanoscale liquid droplets by friction of a solid is observed in real-time. This is achieved using a newly developed in situ transmission electron microscope (TEM) triboprobe capable of applying multiple reciprocating wear cycles to a nanoscale surface. Dynamical imaging of the nanoscale cyclic rubbing of a focused-ion-beam (FIB) processed Al alloy by diamond shows that the generation of nanoscale wear particles is followed by a phase separation to form liquid Ga nanodroplets and liquid bridges. The transformation of a two-body system to a four-body solid-liquid system within the reciprocating wear track significantly alters the local dynamical friction and wear processes. Moving liquid bridges are observed in situ to play a key role at the sliding nanocontact, interacting strongly with the highly mobile nanoparticle debris. In situ imaging demonstrates that both static and moving liquid droplets exhibit asymmetric menisci due to nanoscale surface roughness. Nanodroplet kinetics are furthermore dependent on local frictional temperature, with solid-like surface nanofilaments forming on cooling. TEM nanotribology opens up new avenues for the real-time quantification of cyclic friction, wear and dynamic solid-liquid nanomechanics, which will have widespread applications in many areas of nanoscience and nanotechnology.

Analysis of Hydrogen Bonding and Stability of Protein Secondary Structures in Molecular Dynamics Simulation

Molecular Dynamics (MD) simulations provide an atomic level account of the molecular motions and have proven to be immensely useful in the investigation of the dynamical structure of proteins. Once an MD trajectory is obtained, specific interactions at the molecular level can be directly studied by setting up appropriate combinations of distance and angle monitors. However, if a study of the dynamical behavior of secondary structures in proteins becomes important, this approach can become unwieldy. We present herein a method to study the dynamical stability of secondary structures in proteins, based on a relatively simple analysis of backbone hydrogen bonds. The method was developed for studying the thermal unfolding of beta-lactamases, but can be extended to other systems and adapted to study relevant properties.

Correlations, quantum entanglement and interference in nanoscopic systems

Several of the most interesting quantum effects can or could be observed in nanoscopic systems. For example, the effect of strong correlations between electrons and of quantum interference can be measured in transport experiments through quantum dots, wires, individual molecules and rings formed by large molecules or arrays of quantum dots. In addition, quantum coherence and entanglement can be clearly observed in quantum corrals. In this paper we present calculations of transport properties through Aharonov-Bohm strongly correlated rings where the characteristic phenomenon of charge-spin separation is clearly observed. Additionally quantum interference effects show up in transport through pi-conjugated annulene molecules producing important effects on the conductance for different source-drain configurations, leading to the possibility of an interesting switching effect. Finally, elliptic quantum corrals offer an ideal system to study quantum entanglement due to their focalizing properties. Because of an enhanced interaction between impurities localized at the foci, these systems also show interesting quantum dynamical behaviour and offer a challenging scenario for quantum information experiments.

Shear alignment of a disordered lamellar mesophase

The shear alignment of an initially disordered lamellar phase is examined using lattice Boltzmann simulations of a mesoscopic model based on a free-energy functional for the concentration modulation. For a small shear cell of width 8 lambda, the qualitative features of the alignment process are strongly dependent on the Schmidt number Sc = nu/D (ratio of kinematic viscosity and mass diffusion coefficient). Here, lambda is the wavelength of the concentration modulation. At low Schmidt number, it is found that there is a significant initial increase in the viscosity, coinciding with the alignment of layers along the extensional axis, followed by a decrease at long times due to the alignment along the flow direction. At high Schmidt number, alignment takes place due to the breakage and reformation of layers because diffusion is slow compared to shear deformation; this results in faster alignment. The system size has a strong effect on the alignment process; perfect alignment takes place for a small systems of width 8 lambda and 16 lambda, while a larger system of width 32 lambda does not align completely even at long times. In the larger system, there appears to be a dynamical steady state in which the layers are not perfectly aligned-where there is a balance between the annealing of defects due to shear and the creation due to an instability of the aligned lamellar phase under shear. We observe two types of defect creation mechanisms: the buckling instability under dilation, which was reported earlier, as well as a second mechanism due to layer compression.

Xenon in sodium Y zeolite. 2. Arrhenius relation, mechanism, and barrier height distribution for cage-to-cage diffusion

Various geometrical and energetic distribution functions and other properties connected with the cage-to-cage diffusion of xenon in sodium Y zeolite have been obtained from long molecular dynamics calculations. Analysis of diffusion pathways reveals two interesting mechanisms-surface-mediated and centralized modes for cage-to-cage diffusion. The surface-mediated mode of diffusion exhibits a small positive barrier, while the centralized diffusion exhibits a negative barrier for the sorbate to diffuse across the 12-ring window. In both modes, however, the sorbate has to be activated from the adsorption site to enable it to gain mobility. The centralized diffusion additionally requires the sorbate to be free of the influence of the surface of the cage as well. The overall rate for cage-to-cage diffusion shows an Arrhenius temperature dependence with E(a) = 3 kJ/mol. It is found that the decay in the dynamical correction factor occurs on a time scale comparable to the cage residence time. The distributions of barrier heights have been calculated. Functions reflecting the distribution of the sorbate-zeolite interaction at the window and the variations of the distance between the sorbate and the centers of the parent and daughter cages are presented.

Formation and propagation of bands in jerky flow:a coupled lattice map description

There has been revival of interest in Jerky flow from the point of view of dynamical systems. The earliest attempt in this direction was from our group. One of the predictions of the theory is that Jerky flow could be chaotic. This has been recently verified by us. We have recently extended the earlier model to account for the spatial aspect as well. Both these models are in the form of coupled set of nonlinear differential equations and hence, they are complicated in their structure. For this reason we wish to devise a model based on the results of these two theories in the form of coupled lattice map for the description of the formation and propagation of dislocation bands. We report here one such model and its results.

Crossover dynamics at large metastability in gas-liquid nucleation

We have developed an alternate description of dynamics of nucleation in terms of an extended set of order parameters. The order parameters consist of an ordered set of kth largest clusters, ordered such that k = 1 is the largest cluster in the system, k = 2 is the second largest cluster, and so on. We have derived an analytic expression for the free energy for the kth largest cluster, which is in excellent agreement with the simulated results. At large supersaturation, the free energy barrier for the growth of the kth largest cluster disappears and the nucleation becomes barrierless. The major success of this extended theoretical formalism is that it can clearly explain the observed change in mechanism at large metastability P. Bhimalapuram et al., Phys. Rev. Lett. 98, 206104 (2007)] and the associated dynamical crossover. The classical nucleation theory cannot explain this crossover. The crossover from activated to barrierless nucleation is found to occur at a supersaturation where multiple clusters cross the critical size. We attribute the crossover as the onset of the kinetic spinodal. We have derived an expression for the rate of nucleation in the barrierless regime by modeling growth as diffusion on the free energy surface of the largest cluster. The model reproduces the slower increase in the rate of growth as a function of supersaturation, as observed in experiments.

A novel neural network design for long range prediction of rainfall pattern

The importance of long-range prediction of rainfall pattern for devising and planning agricultural strategies cannot be overemphasized. However, the prediction of rainfall pattern remains a difficult problem and the desired level of accuracy has not been reached. The conventional methods for prediction of rainfall use either dynamical or statistical modelling. In this article we report the results of a new modelling technique using artificial neural networks. Artificial neural networks are especially useful where the dynamical processes and their interrelations for a given phenomenon are not known with sufficient accuracy. Since conventional neural networks were found to be unsuitable for simulating and predicting rainfall patterns, a generalized structure of a neural network was then explored and found to provide consistent prediction (hindcast) of all-India annual mean rainfall with good accuracy. Performance and consistency of this network are evaluated and compared with those of other (conventional) neural networks. It is shown that the generalized network can make consistently good prediction of annual mean rainfall. Immediate application and potential of such a prediction system are discussed.

Carbon-13 relaxation study of chain segmental motion and side-chain internal rotations of poly(isobutyl methacrylate) in solution

The dynamics of poly(isobutyl methacrylate) in toluene solution has been examined by C-13 spin-lattice relaxation time and NOE measurements as a function of temperature. The experiments were performed at 50.3 and 100.6 MHz. The backbone carbon relaxation data have been analyzed using the Dejean-Laupretre-Monnerie (DLM) model, which describes the dynamical processes in the backbone in terms of conformational transitions and bond librations. The relaxation data of the side chain nuclei have been analyzed by assuming different motional models, namely, unrestricted rotational diffusion, three site jumps, and restricted rotational diffusion. The different models have been compared for their ability to reproduce the experimental spin-lattice relaxation times and also to predict the behavior of NOE as a function of temperature. Conformational energy calculations have been carried out on a model compound by using the semiempirical quantum chemical method, AM1, and the results confirm the validity of the motional models used to describe the side-chain motion.

Molecular dynamics investigation of sorption of argon in NaCaA zeolite

A molecular dynamics calculation of argon in NaCaA zeolite at 393 K and 1 atom per cage is reported. Equilibrium properties such as guest-host interaction energy, guest-guest dimerization and bonding energy, various guest-host and guest-guest radial distribution functions and dynamical properties such as the mean-square displacement, power spectra and diffusion coefficient have been obtained.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

Perturbative growth of cosmological clustering .2. The two-point correlation

We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two-point correlation and the pair velocity for Gaussian initial conditions in a critical density matter-dominated cosmological model. We compare our results with the results obtained using the hydrodynamic equations that neglect pressure and find that the two match, indicating that there are no effects of multistreaming at this order of perturbation. We analytically study the effect of small scales on the large scales by calculating the nonlinear correction for a Dirac delta function initial two-point correlation. We find that the induced two-point correlation has a x(-6) behavior at large separations. We have considered a class of initial conditions where the initial power spectrum at small k has the form k(n) with 0 < n less than or equal to 3 and have numerically calculated the nonlinear correction to the two-point correlation, its average over a sphere and the pair velocity over a large dynamical range. We find that at small separations the effect of the nonlinear term is to enhance the clustering, whereas at intermediate scales it can act to either increase or decrease the clustering. At large scales we find a simple formula that gives a very good fit for the nonlinear correction in terms of the initial function. This formula explicitly exhibits the influence of small scales on large scales and because of this coupling the perturbative treatment breaks down at large scales much before one would expect it to if the nonlinearity were local in real space. We physically interpret this formula in terms of a simple diffusion process. We have also investigated the case n = 0, and we find that it differs from the other cases in certain respects. We investigate a recently proposed scaling property of gravitational clustering, and we find that the lowest order nonlinear terms cause deviations from the scaling relations that are strictly valid in the linear regime. The approximate validity of these relations in the nonlinear regime in l(T)-body simulations cannot be understood at this order of evolution.