On the stabilization of uniformly decoupled systems by state variable feedback

Conditions under which the asymptotic stabilization of uniformly decoupled time-varying multivariate systems is possible are explored. This is accomplished by developing a canonical form for integrator uniformly decoupled system in which the coefficient matrices have a simple structure. The procedures developed rely on certain conditions on the given system and yield explicit expressions for the stabilization compensators.

Thermodynamic characterization of the reversible, two-state unfolding of maltose binding protein, a large two-domain protein

The folding and stability of maltose binding protein (MBP) have been investigated as a function of pH and temperature by intrinsic tryptophan fluorescence, far- and near-UV circular dichroism, and high-sensitivity differential scanning calorimetric measurements. MBP is a monomeric, two-domain protein containing 370 amino acids. The protein is stable in the pH range of 4-10.5 at 25 degrees C. The protein exhibits reversible, two-state, thermal and guanidine hydrochloride-mediated denaturation at neutral pH. The thermostability of MBP is maximal at pH 6, with a Tm of 64.9 degrees C and a deltaHm of 259.7 kcal mol(-1). The linear dependence of deltaHm on Tm was used to estimate a value of deltaCp of 7.9 kcal mol(-1) K(-1) or 21.3 cal (mol of residue)(-1) K(-1). These values are higher than the corresponding deltaCp's for most globular proteins studied to date. However, the extrapolated values of deltaH and deltaS (per mole of residue) at 110 degrees C are similar to those of other globular proteins. These data have been used to show that the temperature at which a protein undergoes cold denaturation depends primarily on the deltaCp (per mol of residue) and that this temperature increases with an increase in deltaCp. The predicted decrease in stability of MBP at low temperatures was experimentally confirmed by carrying out denaturant-mediated unfolding studies at neutral pH at 2 and 28 degrees C.

Crystal state conformation of three model monomer units for the beta-bend ribbon structure

The molecular and crystal structures of three compounds, representing the repeating units of the -bend ribbon (an approximate 310-helix, with an intramolecular hydrogen-bonding donor every two residues), have been determined by x-ray diffraction. They are Boc-Aib-Hib-NHBzl, Z-Aib-Hib-NHBzl, and Z-L-Hyp-Aib-NHMe (Aib, -aminoisobutyric acid; Bzl, benzyl; Boc, t-butyloxycarbonyl; Hyp, hydroxyproline Hib, -hydroxyisobutyric acid; Z, benzyloxycarbonyl). The two former compounds are folded in a -bend conformation: type III (III) for Boc-Aib-Hib-NHBzl, while type II (II) for the Z analogue. Conversely, the structure of Z-L-Hyp-Aib-NHMe, although not far from a type II -bend, is partially open.

X-ray studies on crystalline complexes involving amino acids and peptides. XXIII. Variability in ionization state, conformation and molecular aggregation in the complexes of succinic acid with DL- and L-lysine

Crystalline complexes of succinic acid with DL- and L-lysine have been prepared and analysed by X-ray diffraction. DL-Lysine complex: C6HIsN202 + 1 2- 1 ~C4H404 .~C4H604, Mr -- 264"2, PI, a = 5"506 (4), =8.070(2), c=14.089(2) A,, a=92.02(1), /3= 100"69 (3), y = 95"85 (3) ~>, Z = 2, Dx = 1"44 g cm -3, R = 0.059 for 2546 observed reflections. Form I of the e-lysine complex: C6HIsN20-, ~ .C4H504, Mr = 264.2, P1, a = 5" 125 (2), b = 8"087 (1), c = 8"689 (1) A,, a = 112.06 (1), /3 = 99.08 (2), y = 93"77(2) °, Z--l, D,,,=1"34(3), Dx=l"34gcm 3 R = 0.033 for 1475 observed reflections. Form II of + I 2- the e-lysine complex: C6H15N202 .,iC4H404 .- 1 I ") 4C4H604.4(C4HsO4""H'"CaH404)" , Mr = 264"2, P1, a = 10.143 (4), b = 10.256 (2), c = 12"916 (3) A,, a = 105.00 (2),/3 = 99-09 (3), y = 92"78 (3)::, Z = 4, Dm= 1"37(4), D,.= 1.38gcm 3, R=0.067 for 2809 observed reflections. The succinic acid molecules in the structures exhibit a variety of ionization states. Two of the lysine conformations found in the complexes have been observed for the first time in crystals containing lysine. Form II of the L-lysine complex is highly pseudosymmetric. In all the complexes, unlike molecules aggregate into separate alternating layers. The basic element of aggregation in the lysine layer in the complexes is an S2-type head-to-tail sequence. This element combines in different ways in the three structures. The basic element of aggre gation in the succinic acid layer in the complexes is a hydrogen-bonded ribbon. The ribbons are interconnected indirectly through amino groups in the lysine layer.

Underwater Sustainability of the ``Cassie'' State of Wetting

A rough hydrophobic surface when immersed in water can result in a ``Cassie'' state of wetting in which the water is in contact with both the solid surface and the entrapped air. The sustainability of the entrapped air on such surfaces is important for underwater applications such as reduction of flow resistance in microchannels and drag reduction of submerged bodies such as hydrofoils. We utilize an optical technique based oil total internal reflection of light at the water-air interface to quantify the spatial distribution of trapped air oil such a surface and its variation with immersion time. With this technique, we evaluate the sustainability of the Cassie state on hydrophobic surfaces with four different kinds of textures. The textures studied are regular arrays of pillars, ridges, and holes that were created in silicon by a wet etching technique, and also a texture of random craters that was obtained through electrodischarge machining of aluminum. These surfaces were rendered hydrophobic with a self-assembled layer Of fluorooctyl trichlorosilane. Depending on the texture, the size and shape of the trapped air pockets were found to vary. However, irrespective of the texture, both the size and the number of air pockets were found to decrease with time gradually and eventually disappear, suggesting that the sustainability of the ``Cassie'' state is finite for all the microstructures Studied. This is possibly due to diffusion of air from the trapped air pockets into the water. The time scale for disappearance of air pockets was found to depend on the kind of microstructure and the hydrostatic pressure at the water-air interface. For the surface with a regular array of pillars, the air pockets were found to be in the form of a thin layer perched on top of the pillars with a large lateral extent compared to the spacing between pillars. For other surfaces studied, the air pockets are smaller and are of the same order as the characteristic length scale of the texture. Measurements for the surface with holes indicate that the time for air-pocket disappearance reduces as the hydrostatic pressure is increased.

Spinodal Decomposition in Tellurite-Based Glasses Induced by Excimer Laser Irradiation

Tellurite-based glasses in the TeO2-K3Li2Nb5O15, TeO2-Ba5Li2Ti2Nb8O30, and V2Te2O9 were fabricated by the conventional melt-quenching technique. Amorphous and glassy characteristics of the as-quenched samples were established via the X-ray powder diffraction technique and differential thermal analysis, respectively. The as-quenched samples were irradiated by an excimer laser (248 nm). The effect of laser power, duration of irradiation, and the frequency of the laser pulses on the surface features of the above glasses were studied. The optical microscopic studies carried out on the above systems revealed the presence of quasi-periodic and periodic structures on their surfaces. The local compositional variations of these structures were confirmed by back-scattered electron imaging using scanning electron microscope accompanied by energy-dispersive X-ray analysis. These results were convincing enough to state that the glasses in the present investigations had undergone spinodal decomposition on laser irradiation. The incidence of the interconnected texture of two different phases was observed owing to the quenching effect produced by the heating and cooling cycle of the successive laser pulses. Ring- and line-shaped patterns were also observed, respectively, when the pulse frequency of the laser and the duration of irradiation were increased.

Trifurcated (four-center) hydrogen bond in solid state crystal structure of 5'-amino-5'-deoxyadenosine p-toluenesulfonate

The crystal structure of 5'-amino-5'-deoxyadenosine (5'-Am.dA) p-toluenesulfonate has been determined by X-ray crystallographic methods. It belongs to the orthorhombic space group P2(1)2(1)2(1) with a = 7.754(3)Angstrom, b = 8.065(1)Angstrom and c = 32.481(2)Angstrom. This nucleoside side shows a syn conformation about the glycosyl bond and C2'-endo-C3'-exo puckering for the ribose sugar. The orientation of N5' atom is gauche-trans about the exocyclic C4'-C5' bond. The amino nitrogen N5' forms a trifurcated hydrogen bond with N3, O9T and O4' atoms. Adenine bases form A.A.A triplets through hydrogen bonding between N6, N7 and N1 atoms of symmetry related nucleoside molecules.

Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor

A mathematical model is developed to simulate oxygen consumption, heat generation and cell growth in solid state fermentation (SSF). The fungal growth on the solid substrate particles results in the increase of the cell film thickness around the particles. The model incorporates this increase in the biofilm size which leads to decrease in the porosity of the substrate bed and diffusivity of oxygen in the bed. The model also takes into account the effect of steric hindrance limitations in SSF. The growth of cells around single particle and resulting expansion of biofilm around the particle is analyzed for simplified zero and first order oxygen consumption kinetics. Under conditions of zero order kinetics, the model predicts upper limit on cell density. The model simulations for packed bed of solid particles in tray bioreactor show distinct limitations on growth due to simultaneous heat and mass transport phenomena accompanying solid state fermentation process. The extent of limitation due to heat and/or mass transport phenomena is analyzed during different stages of fermentation. It is expected that the model will lead to better understanding of the transport processes in SSF, and therefore, will assist in optimal design of bioreactors for SSF.

Semi-active vibration isolation using a near-zero-spring-rate device:steady state analysis of a single-degree-of-freedom model

A vibration isolator is described which incorporates a near-zero-spring-rate device within its operating range. The device is an assembly of a vertical spring in parallel with two inclined springs. A low spring rate is achieved by combining the equivalent stiffness in the vertical direction of the inclined springs with the stiffness of the vertical central spring. It is shown that there is a relation between the geometry and the stiffness of the individual springs that results in a low spring rate. Computer simulation studies of a single-degree-of-freedom model for harmonic base input show that the performance of the proposed scheme is superior to that of the passive schemes with linear springs and skyhook damping configuration. The response curves show that, for small to large amplitudes of base disturbance, the system goes into resonance at low frequencies of excitation. Thus, it is possible to achieve very good isolation over a wide low-frequency band. Also, the damper force requirements for the proposed scheme are much lower than for the damper force of a skyhook configuration or a conventional linear spring with a semi-active damper.

Role of the triplet state in the green emission peak of polyfluorene films: A time evolution study

The blue emission of ethyl-hexyl substituted polyfluorene (PF2/6) films is accompanied by a low energy green emission peak around 500 nm in inert atmosphere. The intensity of this 500 nm peak is large in electroluminescence (EL) compared to photoluminescence (PL)measurements. Furthermore, the green emission intensity reduces dramatically in the presence of molecular oxygen. To understand this, we have modeled various nonradiative processes by time dependent quantum many body methods. These are (i) intersystem crossing to study conversion of excited singlets to triplets leading to a phosphorescence emission, (ii) electron-hole recombination (e-hR) process in the presence of a paramagnetic impurity to follow the yield of triplets in a polyene system doped with paramagnetic metal atom, and (iii) quenching of excited triplet states in the presence of oxygen molecules to understand the low intensity of EL emission in ambient atmosphere, when compared with that in nitrogen atmosphere. We have employed the Pariser-Parr-Pople Hamiltonian to model the molecules and have invoked electron-electron repulsions beyond zero differential approximation while treating interactions between the organic molecule and the rest of the system. Our time evolution methods show that there is a large cross section for triplet formation in the e-hR process in the presence of paramagnetic impurity with degenerate orbitals. The triplet yield through e-hR process far exceeds that in the intersystem crossing pathway, clearly pointing to the large intensity of the 500 nm peak in EL compared to PL measurements. We have also modeled the triplet quenching process by a paramagnetic oxygen molecule which shows a sizable quenching cross section especially for systems with large sizes. These studies show that the most probable origin of the experimentally observed low energy EL emission is the triplets.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present Study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive-frictional soil slope of 30 degrees, a range of coefficients of variation (CoV%) from 60 to 90% in the permeability Values, and taking different values of correlation distance in the range of 0.5-15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect ostochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit's) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties. (C) 2009 Elsevier B.V. All rights reserved.

Buckled nano rod - a two state system: quantum effects on its dynamics

We consider a suspended elastic rod under longitudinal compression. The compression can be used to adjust potential energy for transverse displacements from the harmonic to the double well regime. The two minima in potential energy curve describe two possible buckled states. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain epsilon = 4 epsilon c the simple TST rate diverges. We suggest a method to correct this divergence for quantum calculations. We also find that zero point energy contributions can be quite large so that single mode calculations can lead to large errors in the rate.