Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Viscoelastic Properties of Nanocrystalline Films of Semiconducting Chalcogenides at Liquid/Liquid Interface

The interfacial shear rheological properties of a continuous single-crystalline film of CuS and a 3D particulate gel of CdS nanoparticles (3−5 nm in diameter) formed at toluene−water interfaces have been studied. The ultrathin films (50 nm in thickness) are formed in situ in the shear cell through a reaction at the toluene−water interface between a metal−organic compound in the organic layer and an appropriate reagent for sulfidation in the aqueous layer. Linear viscoelastic spectra of the nanofilms reveal solid-like rheological behavior with the storage modulus higher than the loss modulus over the range of angular frequencies probed. Large strain amplitude sweep measurements on the CdS nanofilms formed at different reactant concentrations suggest that they form a weakly flocculated gel. Under steady shear, the films exhibit a yield stress, followed by a steady shear thinning at high shear rates. The viscoelastic and flow behavior of these films that are in common with those of many 3D “soft” materials like gels, foams, and concentrated colloidal suspensions can be described by the “soft” glassy rheology model.

Quantization noise in binary holograms

The signal-to-noise (S/N) ratio in the reconstructed image from a binary hologram has been quantitatively related to the amplitude and phase quantization levels. The S/N ratio increases monotonically with increasing number of quantization levels. This observation is further supported by experimental results.

Nonlinear surface acoustic waves on an isotropic solid

A systematic derivation of the approximate coupled amplitude equations governing the propagation of a quasi-monochromatic Rayleigh surface wave on an isotropic solid is presented, starting from the non-linear governing differential equations and the non-linear free-surface boundary conditions, using the method of mulitple scales. An explicit solution of these equations for a signalling problem is obtained in terms of hyperbolic functions. In the case of monochromatic excitation, it is shown that the second harmonic amplitude grows initially at the expense of the fundamental and that the amplitudes of the fundamental and second harmonic remain bounded for all time.

Improved damping capacity and machinability of graphite particle-aluminum alloy composites

The damping capacity of cast graphitic aluminum alloy composites has been measured using a torsion pendulum at a constant strain amplitude. It was found that flake-graphite particles dispersed in the matrix of aluminum alloys increased the damping capacity; the improvement was greater, the higher the amount of graphite dispersed in the matrix. At sufficiently high graphite contents the damping capacity of graphitic aluminum composites approaches that of cast iron. The ratio between the damping capacity and the density of graphitic aluminum alloys is higher than cast iron, making them very attractive as light-weight, high-damping materials for possible aircraft applications. Machinability tests on graphite particle-aluminum composites, conducted at speeds of 315 sfm and 525 sfm, showed that the chip length decreased with the amount of graphite of a given size. When the size of graphite was decreased, at a given machining speed, the chip length decreased. Metallographic examination shows that graphite particles act as chip breakers, and are frequently sheared parallel to the plane of the

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Waves in branched hydraulic pipes

The paper deals with the classical problem of axi-symmetric transmission of low amplitude waves through a circular pipe containing a viscous liquid. Exact governing equations are identified and solved, the radial as well as the axial component of the velocity being considered. Attention is drawn to certain fallacies underlying the conventional approach. The parameters required in the formulation of the transfer matrix for a pipe have been evaluated. In order to evaluate the response at the terminal point of a branched system for a sinusoidal input at one of the ends, a general algorithm has been developed.

Diurnal variation of anterior scleral and conjunctival thickness

Purpose To examine whether anterior scleral and conjunctival thickness undergoes significant diurnal variation over a 24-hour period. Methods Nineteen healthy young adults (mean age 22 ± 2 years) with minimal refractive error (mean spherical equivalent refraction -0.08 ± 0.39 D), had measures of anterior scleral and conjunctival thickness collected using anterior segment optical coherence tomography (AS-OCT) at seven measurement sessions over a 24-hour period. The thickness of the temporal anterior sclera and conjunctiva were determined at 6 locations (each separated by 0.5 mm) at varying distances from the scleral spur for each subject at each measurement session. Results Both the anterior sclera and conjunctiva were found to undergo significant diurnal variations in thickness over a 24-hour period (both p <0.01). The sclera and conjunctiva exhibited a similar pattern of diurnal change, with a small magnitude thinning observed close to midday, and a larger magnitude thickening observed in the early morning immediately after waking. The amplitude of diurnal thickness change was larger in the conjunctiva (mean amplitude 69 ± 29 μm) compared to the sclera (21 ± 8 μm). The conjunctiva exhibited its smallest magnitude of change at the scleral spur location (mean amplitude 56 ± 17 μm) whereas the sclera exhibited its largest magnitude of change at this location (52 ± 21 μm). Conclusions This study provides the first evidence of diurnal variations occurring in the thickness of the anterior sclera and conjunctiva. Studies requiring precise measures of these anatomical layers should therefore take time of day into consideration. The majority of the observed changes occurred in the early morning immediately after waking and were of larger magnitude in the conjunctiva compared to the sclera. Thickness changes at other times of the day were of smaller magnitude and generally not statistically significant.

Nature of trapped particle instability

The amplification mechanism for the side bands which accompany a large amplitude electron wave on a plasma column are shown to arise due to two mode interaction between negative and positive energy waves.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

FSK bursts for efficient clutter rejection

The clutter-rejection properties of compact f.s.k. bursts with amplitude modulation are investigated. A procedure for computer-aided design of such signals is given. The loss of clutter performance on constraining the individual pulse amplitudes to be equal is evaluated.

The structure of turbulent boundary layers along mildly curved surfaces

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers. (Published Online April 12 2006)

Essays on macroeconomic effects of fiscal policy rules

Economic and Monetary Union can be characterised as a complicated set of legislation and institutions governing monetary and fiscal responsibilities. The measures of fiscal responsibility are to be guided by the Stability and Growth Pact, which sets rules for fiscal policy and makes a discretionary fiscal policy virtually impossible. To analyse the effects of the fiscal and monetary policy mix, we modified the New Keynesian framework to allow for supply effects of fiscal policy. We show that defining a supply-side channel for fiscal policy using an endogenous output gap changes the stabilising properties of monetary policy rules. The stability conditions are affected by fiscal policy, so that the dichotomy between active (passive) monetary policy and passive (active) fiscal policy as stabilising regimes does not hold, and it is possible to have an active monetary - active fiscal policy regime consistent with dynamical stability of the economy. We show that, if we take supply-side effects into ac-count, we get more persistent inflation and output reactions. We also show that the dichotomy does not hold for a variety of different fiscal policy rules based on government debt and budget deficit, using the tax smoothing hypothesis and formulating the tax rules as difference equations. The debt rule with active monetary policy results in indeterminacy, while the deficit rule produces a determinate solution with active monetary policy, even with active fiscal policy. The combination of fiscal requirements in a rule results in cyclical responses to shocks. The amplitude of the cycle is larger with more weight on debt than on deficit. Combining optimised monetary policy with fiscal policy rules means that, under a discretionary monetary policy, the fiscal policy regime affects the size of the inflation bias. We also show that commitment to an optimal monetary policy not only corrects the inflation bias but also increases the persistence of output reactions. With fiscal policy rules based on the deficit we can retain the tax smoothing hypothesis also in a sticky price model.

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.