Nonlinear aeroelasticity of rotating and flapping wings - a review

The interaction between large deflections, rotation effects and unsteady aerodynamics makes the dynamic analysis of rotating and flapping wing a nonlinear aeroelastic problem. This problem is governed by nonlinear periodic partial differential equations whose solution is needed to calculate the response and loads acting on vehicles using rotary or flapping wings for lift generation. We look at three important problems in this paper. The first problem shows the effect of nonlinear phenomenon coming from piezoelectric actuators used for helicopter vibration control. The second problem looks at the propagation on material uncertainty on the nonlinear response, vibration and aeroelastic stability of a composite helicopter rotor. The third problem considers the use of piezoelectric actuators for generating large motions in a dragonfly inspired flapping wing. These problems provide interesting insights into nonlinear aeroelasticity and show the likelihood of surprising phenomenon which needs to be considered during the design of rotary and flapping wing vehicle

Kinetics and the mechanism of interaction of the endoplasmic reticulum chaperone, calreticulin, with monoglucosylated (Glc(1)Man(9)GlcNAc(2)) substrate

Calreticulin is a lectin-like molecular chaperone of the endoplasmic reticulum in eukaryotes. Its interaction with N-glycosylated polypeptides is mediated by the glycan, Glc(1)Man(9)GlcNAc(2), present on the target glycoproteins. In this work, binding of monoglucosyl IgG (chicken) substrate to calreticulin has been studied using real time association kinetics of the interaction with the biosensor based on surface plasmon resonance (SPR). By SPR, accurate association and dissociation rate constants were determined, and these yielded a micromolar association constant. The nature of reaction was unaffected by immobilization of either of the reactants. The Scatchard analysis values for K-a agreed web crith the one obtained by the ratio k(1)/k(-1). The interaction was completely inhibited by free oligosaccharide, Glc(1)Man(9)GlcNAc(2), whereas Man(9)GlcNAc(2) did not bind to the calreticulin-substrate complex, attesting to the exquisite specificity of this interaction. The binding of calreticulin to IgG was used for the development of immunoassay and the relative affinity of the lectin-substrate association was indirectly measured. The values are in agreement with those obtained with SPR. Although the reactions are several orders of magnitude slower than the diffusion controlled processes, the data are qualitatively and quantitatively consistent with single-step bimolecular association and dissociation reaction. Analyses of the activation parameters indicate that reaction is enthalpically driven and does not involve a highly ordered transition state. Based on these data, the mechanism of its chaperone activity is briefly discussed.

Hysteresis in model spin systems

The authors study the hysteretic response of model spin systems to periodic time-varying fields H(t) as a function of the amplitude H0 and the frequency Omega . At fixed H0, they find conventional, squarish hysteresis loops at low Omega , and rounded, roughly elliptical loops at high Omega , in agreement with experiment. For the O(N to infinity ), d=3, ( Phi 2)2 model with Langevin dynamics, they find a novel scaling behaviour for the area A of the hysteresis loop, of the form (valid for low fields) A approximately=H0066 Omega 0.33.

Analysis of solar radiation pressure induced coupled liberations of a gravity stabilized axisymmetric satellite

This paper presents an analysis of solar radiation pressure induced coupled librations of gravity stabilized cylindrical spacecraft with a special reference to geostationary communication satellites. The Lagrangian approach is used to obtain the corresponding equations of motion. The solar induced torques are assumed to be free of librational angles and are represented by their Fourier expansion. The response and periodic solutions are obtained through linear and nonlinear analyses, using the method of harmonic balance in the latter case. The stability conditions are obtained using Routh-Hurwitz criteria. To establish the ranges of validity the analytic response is compared with the numerical solution. Finally, values of the system parameters are suggested to make the satellite behave as desired. Among these is a possible approach to subdue the solar induced roll resonance. It is felt that the approximate analysis presented here should significantly reduce the computational efforts involved in the design and stability analysis of the systems.

Nonlinear intrinsic instability of solid propellant combustion including gas-phase thermal inertia

The problem of homogeneous solid propellant combustion instability is studied with a one-dimensional flame model, including the effects of gas-phase thermal inertia and nonlinearity. Computational results presented in this paper show nonlinear instabilities inherent in the equations, due to which periodic burning is found even under steady ambient conditions such as pressure. The stability boundary is obtained in terms of Denison-Baum parameters. It is found that inclusion of gas-phase thermal inertia stabilizes the combustion. Also, the effect of a distributed heat release in the gas phase, compared to the flame sheet model, is to destabilize the burning. Direct calculations for finite amplitude pressure disturbances show that two distinct resonant modes exist, the first one near the natural frequency as obtained from intrinsic instability analysis and a second mode occurring at a much higher driving frequency. It is found that er rn in the low frequency region, the response of the propellant is significantly affected by the specific type of gas-phase chemical heat-release model employed. Examination of frequency response function reveals that the role of gas-phase thermal inertia is to stabilize the burning near the first resonant mode. Calculations made for different amplitudes of driving pressure show that the mean burning rate decreases with increasing amplitude. Also, with an increase in the driving amplitude, higher harmonics are generated in the burning rate.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

Characterization of poly(ADP-ribosyl)ated domains of rat pachytene chromatin

Poly(ADP-ribosyl)ation of nuclear proteins was several-fold higher in the pachytene spermatocytes than in the premeiotic germ cells of the rat. Among the histones of the pachytene nucleus, histone subtypes H2A, H1 and H3 were poly(ADP-ribosyl)ated. Based on the immunoaffinity fractionation procedure of Malik, Miwa, Sugimara & Smulson [(1983) Proc. Natl. Acad. Sci. U.S.A. 80, 2554-2558] we have fractionated DNAase-II-solubilized chromatin into poly(ADP-ribosyl)ated chromatin (PAC) and non-poly(ADP-ribosyl)ated chromatin (non-PAC) domains on an anti-[poly(ADP-ribose)] IgG affinity matrix. Approx. 2.5% of the pachytene chromatin represented the PAC domains. A significant amount of [alpha-32P]dATP-labelled pachytene chromatin (labelled in vitro) was bound to the affinity matrix. The DNA of pachytene PAC domains had internal strand breaks, significant length of gaps and ligatable ends, namely 5'-phosphoryl and 3'-hydroxyl termini. On the other hand, the PAC domains from 18 h regenerating liver had very few gaps, if any. The presence of gaps in the pachytene PAC DNA was also evident from thermal denaturation studies. Although many of the polypeptides were common to the PAC domains of both pachytene and regenerating liver, the DNA sequences associated with these domains were quite different. A 20 kDa protein and the testis-specific histone H1t were selectively enriched in the pachytene PAC domains. The pachytene PAC domains also contained approx. 10% of the messenger coding sequences present in the DNAase-II-solubilized chromatin. The pachytene PAC domains, therefore, may represent highly enriched DNA-repair domains of the pachytene nucleus.

Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

We recently introduced the dynamical cluster approximation (DCA), a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, Phi derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

Undamped oscillations of homogeneous collisionless stellar systems

The Lewis (1968) invariant of the time-dependent harmonic oscillator is used to construct exact time-dependent, uniform density solutions of the collisionless Boltzmann equation. The spatially bound solutions are time-periodic.

An unusual C-H center dot center dot center dot O hydrogen bond mediated reversal of polypeptide chain direction in a synthetic peptide helix

An unusual C-terminal conformation has been detected in a synthetic decapeptide designed to analyze the stereochemistry of helix termination in polypeptides. The crystal structure of the decapeptide Boc-Leu-Aib-Val-Ala-Leu-Aib-Val-(D)Ala-(D)Leu-Aib-OMe reveals a helical segment spanning residues 1-7 and helix termination by formation of a Schellman motif, generated by (D)Ala(8) adopting the left-handed helical (alpha(L)) conformation. The extended conformation at (D)Leu(9) results in a compact folded structure, stabilized by a potentially strong C-H ... O hydrogen bond between Ala(4) (CH)-H-alpha and (D)Leu(9)CO. The parameters for C-H ... O interaction are Ala(4) (CH)-H-alpha .. O=C (D)Leu(9) distance 3.27 Angstrom C-alpha-H .. O angle 176 degrees, and O .. H-alpha distance 2.29 Angstrom. This structure suggests that insertion of contiguous D-residues may provide a handle for the generation of designed structures containing more than one helical segment folded in a compact manner. (C) 2000 Academic Press.

Nonlinear measures of heart rate time series: influence of posture and controlled breathing

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P<0.00001), a decrease in predictability (P<0.00001) and an increase in nonlinearity (P=0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component. (C) 2000 published by Elsevier Science B.V.

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

The behaviour of excited plane jets

A plane subsonic jet can be excited to entrain more fluid from its surroundings by subjecting it to antisymmetric periodic disturbances. The essential feature in this phenomenon is the rolling-up motion of an initially flapping jet to form large vortices which are responsible for greater entrainment. Several methods developed to impart oscillations to the flow at the nozzle, such as the acoustic pressure oscillator, the vibration of a single vane in the potential core region, the reciprocating lip system and the twin vane exciter, are described in this article. A minimum threshold in amplitude is necessary for exciting the flow. However, the frequency of oscillation is much less than that predicted by stability considerations.

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of noninteracting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials and show that nonadiabatic pumping violates the simple sin phi rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time-reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and nonresonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.