A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

Fluid dynamics of the monsoon

The monsoonal regions of the world are characterized by a seasonal reversal in the direction of winds associated with the excursion of the equatorial trough (or the ITCZ) in response to the variation in the latitude of maximum insolation. This monsoonal circulation is a planetary scale phenomenon. However, the associated precipitation is critically dependent on the organization of the cumulus clouds (typically a few kilometers in horizontal extent) over the scale of synoptic vortices (typically a few hundred kilometers in horizontal extent). Thus modelling of the seasonal transitions and intraseasonal fluctuations requires an understanding of the fluid mechanics of these three scales of organizations and their interactions. The present paper is an attempt to outline the current state of understanding of these phenomena.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.

Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Sulphate ion dynamics in a-alums studied by esr at high pressures

The variation of zero-field splitting and linewidth of Cr3+ ion in KCr and KAI alums with hydrostatic pressure and with temperature is investigated. A model for the apparent phase transition is proposed on the basis of the reorientational motion of the SO2-4 groups.

Regularized numerical integration of multibody dynamics with the generalized alpha method*

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

Proton NMR spectra including 13C- and 77Se-satellites in organoselenium compounds oriented in the nematic phase : Part 1. The spectrum of 2,1,3-benzoselenadiazole

The vibrationally corrected structure of 2,1,3-benzoselenadiazole is derived from the proton NMR spectrum including 13C-H and 77Se-H satellites, in a nematic solvent. The results indicate considerable bond-fixation in the 6-membered ring. References

Neutron Scattering and Molecular Dynamics Evidence for Levitation Effect in Nanopores

Neutron Scattering and Molecular Dynamics Evidence for Levitation Effect in Nanopores ... Neutron scattering measurements and molecular dynamics simulations have been carried out on the three isomers of pentane (neopentane (neo), isopentane (iso), and n-pentane (n-)) adsorbed in zeolite NaY. ... In order to understand this surprising dependence, the dimensionless levitation parameter, γ, for atomic systems may be modified to suit molecular systems.

Hybrid Simulation of Queuing-System Dynamics

This paper presents a simple hybrid computer technique to study the transient behaviour of queueing systems. This method is superior to stand-alone analog or digital solution because the hardware requirement is excessive for analog technique whereas computation time is appreciable in the latter case. By using a hybrid computer one can share the analog hardware thus requiring fewer integrators. The digital processor can store the values, play them back at required time instants and change the coefficients of differential equations. By speeding up the integration on the analog computer it is feasible to solve a large number of these equations very fast. Hybrid simulation is even superior to the analytic technique because in the latter case it is difficult to solve time-varying differential equations.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

Dynamics of a class of social interaction systems

A mathematical model of social interaction in the form of two coupler! first-order non-linear differential equations, forms the topic of this study. This non-conservative model io representative of such varied social interaction problems as coexisting sub-populations of two different species, arms race between two rival countries and the like. Differential transformation techniques developed elsewhere in the literature are seen to be effective tools of dynamic analysis of this non-linear non-conservative mode! of social interaction process.

Dynamics of carbohydrateâlectin interaction The interaction p-nitrophenyl-β-D-galactose with a lectin from Ricinius communis

L&in-induced agglutination is a complex process determined by several factprs such as the nature of lectin (valency, binding constant) the properties of cell membrane (fluidity, distribution of lectin receptor sites) and the metabolic state of the cell (microvilli, microtubules, microfilament) [l-3].

Dynamics of Circulating Concentrations of Gonadotropins and Ovarian Hormones Throughout the Menstrual Cycle in the Bonnet Monkey: Role of Inhibin A in the Regulation of Follicle-Stimulating Hormone Secretion

In higher primates, increased circulating follicle-stimulating hormone (FSH) levels seen during late menstrual cycle and during menstruation has been suggested to be necessary for initiation of follicular growth, recruitment of follicles and eventually culminating in ovulation of a single follicle. With a view to establish the dynamics of circulating FSH secretion with that of inhibin A (INH A) and progesterone (P-4)secretions during the menstrual cycle, blood was collected daily from bonnet monkeys beginning day 1 of the menstrual cycle up to 35 days. Serum INH A levels were low during early follicular phase, increased significantly coinciding with the mid cycle luteinizing hormone (LH) surge to reach maximal levels during the mid luteal phase before declining at the late luteal phase, essentially paralleling the pattern Of P-4 secretion seen throughout the luteal phase. Circulating FSH levels were low during early and mid luteal phases, but progressively increased during the late luteal phase and remained high for few days after the onset of menses. In another experiment, lutectomy performed during the mid luteal phase resulted in significant decrease in INH A concentration within 2 hr (58.3 +/- 2 vs. 27.3 +/- 3 pg/mL), and a 2- to 3-fold rise in circulating FSH levels by 24 hr (0.20 +/- 0.02 vs. 0.53 +/- 0.14 ng/mL) that remained high until 48 hr postlutectomy. Systemic administration of Cetrorelix (150 mu g/kg body weight), a gonadotropin releasing hormone receptor antagonist, at mid luteal phase in monkeys led to suppression of serum INH A and P-4 concentrations 24 hr post treatment, but circulating FSH levels did not change. Administration of exogenous LH, but not FSH, significantly increased INH A concentration. The results taken together suggest a tight coupling between LH and INH A secretion and that INH A is largely responsible for maintenance of low FSH concentration seen during the luteal phase. Am. J. Primatol. 71:817-824, 2009.