Fluctuation-dissipation relation for nonlinear Langevin equations

It is shown that the fluctuation-dissipation theorem is satisfied by the solutions of a general set of nonlinear Langevin equations with a quadratic free-energy functional (constant susceptibility) and field-dependent kinetic coefficients, provided the kinetic coefficients satisfy the Onsager reciprocal relations for the irreversible terms and the antisymmetry relations for the reversible terms. The analysis employs a perturbation expansion of the nonlinear terms, and a functional integral calculation of the correlation and response functions, and it is shown that the fluctuation-dissipation relation is satisfied at each order in the expansion.

Network approach for capturing ligand-induced subtle global changes in protein structures

Ligand-induced conformational changes in proteins are of immense functional relevance. It is a major challenge to elucidate the network of amino acids that are responsible for the percolation of ligand-induced conformational changes to distal regions in the protein from a global perspective. Functionally important subtle conformational changes (at the level of side-chain noncovalent interactions) upon ligand binding or as a result of environmental variations are also elusive in conventional studies such as those using root-mean-square deviations (r.m.s.d.s). In this article, the network representation of protein structures and their analyses provides an efficient tool to capture these variations (both drastic and subtle) in atomistic detail in a global milieu. A generalized graph theoretical metric, using network parameters such as cliques and/or communities, is used to determine similarities or differences between structures in a rigorous manner. The ligand-induced global rewiring in the protein structures is also quantified in terms of network parameters. Thus, a judicious use of graph theory in the context of protein structures can provide meaningful insights into global structural reorganizations upon perturbation and can also be helpful for rigorous structural comparison. Data sets for the present study include high-resolution crystal structures of serine proteases from the S1A family and are probed to quantify the ligand-induced subtle structural variations.

Stability of spatially developing boundary layers in pressure gradients

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of order R(-1) in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to O(R(-1)) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal order R(-1) except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.

Learning the global maximum with parameterized learning automata

A feedforward network composed of units of teams of parameterized learning automata is considered as a model of a reinforcement teaming system. The internal state vector of each learning automaton is updated using an algorithm consisting of a gradient following term and a random perturbation term. It is shown that the algorithm weakly converges to a solution of the Langevin equation implying that the algorithm globally maximizes an appropriate function. The algorithm is decentralized, and the units do not have any information exchange during updating. Simulation results on common payoff games and pattern recognition problems show that reasonable rates of convergence can be obtained.

A two timescale stochastic approximation scheme for simulation-based parametric optimization

A two timescale stochastic approximation scheme which uses coupled iterations is used for simulation-based parametric optimization as an alternative to traditional "infinitesimal perturbation analysis" schemes, It avoids the aggregation of data present in many other schemes. Its convergence is analyzed, and a queueing example is presented.

Lopsidedness in WHISP galaxies I. Rotation curves and kinematic lopsidedness

The frequently observed lopsidedness of the distribution of stars and gas in disc galaxies is still considered as a major problem in galaxy dynamics. It is even discussed as an imprint of the formation history of discs and the evolution of baryons in dark matter haloes. Here, we analyse a selected sample of 70 galaxies from the Westerbork Hi Survey of Spiral and Irregular Galaxies. The Hi data allow us to follow the morphology and the kinematics out to very large radii. In the present paper, we present the rotation curves and study the kinematic asymmetry. We extract the rotation curves of the receding and approaching sides separately and show that the kinematic behaviour of disc galaxies can be classified into five different types: symmetric velocity fields where the rotation curves of the receding and approaching sides are almost identical; global distortions where the rotation velocities of the receding and approaching sides have an offset that is constant with radius; local distortions leading to large deviations in the inner and negligible deviations in the outer parts (and vice versa); and distortions that divide the galaxies into two kinematic systems that are visible in terms of the different behaviour of the rotation curves of the receding and approaching sides, which leads to a crossing and a change in side. The kinematic lopsidedness is measured from the maximum rotation velocities, averaged over the plateau of the rotation curves. This gives a good estimate of the global lopsidedness in the outer parts of the sample galaxies. We find that the mean value of the perturbation parameter denoting the lopsided potential as obtained from the kinematic data is 0.056. Altogether, 36% of the sample galaxies are globally lopsided, which can be interpreted as the disc responding to a halo that was distorted by a tidal encounter. In Paper II, we study the morphological lopsidedness of the same sample of galaxies.

Multiscale stochastic approximation for parametric optimization of hidden Markov models

A two-time scale stochastic approximation algorithm is proposed for simulation-based parametric optimization of hidden Markov models, as an alternative to the traditional approaches to ''infinitesimal perturbation analysis.'' Its convergence is analyzed, and a queueing example is presented.

Prediction of reaeration rates in square, stirred tanks

Experiments were conducted on the oxygen transfer coefficient, k(L)a(20), through surface aeration in geometrically similar square tanks, with a rotor of diameter D fitted with six flat blades. An optimal geometric similarity of various linear dimensions, which produced maximum k(L)a(20) for any rotational speed of rotor N by an earlier study, was maintained. A simulation equation uniquely correlating k = k(L)a(20)(nu/g(2))(1/3) (nu and g are kinematic viscosity of water and gravitational constant, respectively), and a parameter governing the theoretical power per unit volume, X = (ND2)-D-3/(g(4/3)nu(1/3)), is developed. Such a simulation equation can be used to predict maximum k for any N in any size of such geometrically similar square tanks. An example illustrating the application of results is presented. Also, it has been established that neither the Reynolds criterion nor the Froude criterion is singularly valid to simulate either k or K = k(L)a(20)/N, simultaneously in all the sizes of tanks, even through they are geometrically similar. Occurrence of "scale effects" due to the Reynolds and the Froude laws of similitude on both k and K are also evaluated.

Persistent passive hopping and juggling is possible even with plastic collisions

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one-ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attraction is large. These results persist for mildly non-linear springs and non-constant gravity. Although non-collisional damping destroys the periodic motions, small energy injection makes the periodic motions stable, with a two-sided region of attraction. The existence of such special energy conserving solutions for hopping and juggling points to possibly useful strategies for both animals and robots. The lossless motions are demonstrated with a table-top experiment.

Photodissociation dynamics of CH2ICl at 222, 236, 266, 280, and-304 nm

Dynamics of I*(P-2(1/2)) formation from CH2ICl dissociation has-been investigated at five different ultraviolet excitation wavelengths, e.g., 222, 236, 266, 280, and similar to304 nm. The quantum yield of I*((2)p(1/2)) production, phi*, has been measured by monitoring nascent I(P-2(3/2)) and I* concentrations using a resonance enhanced multiphoton ionization detection scheme. The measured quantum yield as a function of excitation energy follows the same trend as that of methyl iodide except at 236 run. The photodissociation dynamics of CH2ICl also involves three upper states similar to methyl iodide, and a qualitative correlation diagram has been constructed to account for the observed quantum yield. From the difference in behavior at 236 nm, it appears that the crossing region between the two excited states ((3)Q(0) and (1)Q(1)) is located near the exit valley away from the Franck Condon excitation region. The B- and C-band transitions do not participate in the dynamics, and the perturbation of the methyl iodide states due to Cl-I interaction is relatively weak at the photolysis wavelengths employed in this investigation.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

Roy equation analysis of ππ scattering

We analyse the Roy equations for the lowest partial waves of elastic ππ scattering. In the first part of the paper, we review the mathematical properties of these equations as well as their phenomenological applications. In particular, the experimental situation concerning the contributions from intermediate energies and the evaluation of the driving terms are discussed in detail. We then demonstrate that the two S-wave scattering lengths a00 and a02 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S- and P-waves is given and it is shown that the threshold parameters of the D- and F-waves are also fixed very sharply in terms of a00 and a20. In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a00,a02) plane. We show that the data on the reactions e+e−→ππ and τ→ππν reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K→ππeν in restricting the allowed range of a00, preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.

Temperature profiles of accretion discs around rapidly rotating strange stars in general relativity: A comparison with neutron stars

We compute the temperature profiles of accretion discs around rapidly rotating strange stars, using constant gravitational mass equilibrium sequences of these objects, considering the full effect of general relativity. Beyond a certain critical value of stellar angular momentum (J), we observe the radius ( $r_{\rm orb}$) of the innermost stable circular orbit (ISCO) to increase with J (a property seen neither in rotating black holes nor in rotating neutron stars). The reason for this is traced to the crucial dependence of ${\rm d}r_{\rm orb}/{\rm d}J$ on the rate of change of the radial gradient of the Keplerian angular velocity at $r_{\rm orb}$ with respect to J. The structure parameters and temperature profiles obtained are compared with those of neutron stars, as an attempt to provide signatures for distinguishing between the two. We show that when the full gamut of strange star equation of state models, with varying degrees of stiffness are considered, there exists a substantial overlap in properties of both neutron stars and strange stars. However, applying accretion disc model constraints to rule out stiff strange star equation of state models, we notice that neutron stars and strange stars exclusively occupy certain parameter spaces. This result implies the possibility of distinguishing these objects from each other by sensitive observations through future X-ray detectors.