Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Effect of Alkyl Chain Arrangement on Conformation and Dynamics in a Surfactant Intercalated Layered Double Hydroxide: Spectroscopic Measurements and MD Simulations

The anionic surfactant dodecyl sulfate (DDS) has been intercalated in an Mg-Al layered double hydroxide (LDH). Monolayer and bilayer arrangements of the alkyl chains of the intercalated surfactant can be engineered by tuning the Al/Mg ratio of the LDH. In both arrangements the anionic headgroup of the surfactant is tethered to the LDH sheets, and consequently translational mobility of the chains is absent. The degrees of freedom of the confined alkyl chains are restricted to changes in conformation. The effects of the arrangement of the intercalated surfactant chains on conformational order and dynamics have been,investigated by spectroscopic measurements and molecular dynamics simulations. Infrared, Raman, and C-13 NMR spectroscopies were used to investigate conformation of the alkyl chains in the monolayer and bilayer arrangements and variable contact time cross-polarization magic angle spinning (VCT CPMAS) NMR measurements to probe molecular motion. The alkyl chains in the monolayer arrangement of the intercalated DDS chains showed considerably greater conformational disorder and faster dynamics as compared to chains in the bilayer arrangement, in spite of the fact that the volume available per chain in the monolayer is smaller than that in the bilayer. Atomistic MD simulations of the two arrangements of the intercalated surfactant were carried out using an isothermal-isobaric ensemble. The simulations are able to reproduce the essential results of the experiment-greater conformational disorder and faster dynamics for the alkyl chains in the monolayer arrangement of the intercalated surfactant. The MD simulations show that these results are a consequence of the fact that the nature of conformational disorder in the two arrangements is different. In the monolayer arrangement the alkyl chains can sustain isolated gauche defects, whereas in the bilayer arrangement gauche conformers occur only as part of a kink a gauche(+) trans gauche(-) sequence.

A perspective of biological supramolecular electron transfer

Electron transfer is an essential activity in biological systems. The migrating electron originates from water-oxygen in photosynthesis and reverts to dioxygen in respiration. In this cycle two metal porphyrin complexes possessing circular conjugated system and macrocyclic pi-clouds, chlorophyll and hems, play a decisive role in mobilising electrons for travel over biological structures as extraneous electrons. Transport of electrons within proteins (as in cytochromes) and within DNA (during oxidative damage and repair) is known to occur. Initial evaluations did not favour formation of semiconducting pathways of delocalized electrons of the peptide bonds in proteins and of the bases in nucleic acids. Direct measurement of conductivity of bulk material and quantum chemical calculations of their polymeric structures also did not support electron transfer in both proteins and nucleic acids. New experimental approaches have revived interest in the process of charge transfer through DNA duplex. The fluorescence on photoexcitation of Ru-complex was found to be quenched by Rh-complex, when both were tethered to DNA and intercalated in the base stack. Similar experiments showed that damage to G-bases and repair of T-T dimers in DNA can occur by possible long range electron transfer through the base stack. The novelty of this phenomenon prompted the apt name, chemistry at a distance. Based on experiments with ruthenium modified proteins, intramolecular electron transfer in proteins is now proposed to use pathways that include C-C sigma-bonds and surprisingly hydrogen bonds which remained out of favour for a long time. In support of this, some experimental evidence is now available showing that hydrogen bond-bridges facilitate transfer of electrons between metal-porphyrin complexes. By molecular orbital calculations over 20 years ago. we found that "delocalization of an extraneous electron is pronounced when it enters low-lying virtual orbitals of the electronic structures of peptide units linked by hydrogen bonds". This review focuses on supramolecular electron transfer pathways that can emerge on interlinking by hydrogen bonds and metal coordination of some unnoticed structures with pi-clouds in proteins and nucleic acids, potentially useful in catalysis and energy missions.

Stability of domain structures in multi-domain proteins

Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR.

Sol-Gel Transition in Dispersions of Layered Double-Hydroxide Nanosheets

Surfactant-intercalated layered double-hydroxide solid Mg-Al LDH-dodecyl sulfate (DDS) undergoes rapid and facile delamination to its ultimate constituent, single sheets of nanometer thickness and micrometer size, in a nonpolar solvent such as toluene to form stable dispersions. The delaminated nanosheets are electrically neutral because the surfactant chains remain tethered to the inorganic layer even on exfoliation. With increasing volume fraction of the solid, the dispersion transforms from a free-flowing sol to a solidlike gel. Here we have investigated the sol-gel transition in dispersions of the hydrophobically modified Mg-Al LDH-DDS in toluene by rheology, SAXS, and (1)H NMR measurements. The rheo-SAXS measurements show that the sharp rise in the viscosity of the dispersion during gel formation is a consequence of a tactoidal microstructure formed by the stacking of the nanosheets with an intersheet separation of 3.92 nm. The origin and nature of the attractive forces that lead to the formation of the tactoidal structure were obtained from 1D and 2D (1)H NMR measurements that provided direct evidence of the association of the toluene solvent molecules with the terminal methyl of the tethered DDS surfactant chains. Gel formation is a consequence of the attractive dispersive interactions of toluene molecules with the tails of DDS chains anchored to opposing Mg-Al LDH sheets. The toluene solvent molecules function as molecular ``glue'' holding the nanosheets within the tactoidal microstructure together. Our study shows how rheology, SAXS, and NMR measurements complement each other to provide a molecular-level description of the sol-gel transition in dispersions of a hydrophobically modified layered double hydroxide.

Fluid Mechanics of Aquatic Locomotion at Large Reynolds Numbers

Abstract | There exist a huge range of fish species besides other aquatic organisms like squids and salps that locomote in water at large Reynolds numbers, a regime of flow where inertial forces dominate viscous forces. In the present review, we discuss the fluid mechanics governing the locomotion of such organisms. Most fishes propel themselves by periodic undulatory motions of the body and tail, and the typical classification of their swimming modes is based on the fraction of their body that undergoes such undulatory motions. In the angulliform mode, or the eel type, the entire body undergoes undulatory motions in the form of a travelling wave that goes from head to tail, while in the other extreme case, the thunniform mode, only the rear tail (caudal fin) undergoes lateral oscillations. The thunniform mode of swimming is essentially based on the lift force generated by the airfoil like crosssection of the fish tail as it moves laterally through the water, while the anguilliform mode may be understood using the “reactive theory” of Lighthill. In pulsed jet propulsion, adopted by squids and salps, there are two components to the thrust; the first due to the familiar ejection of momentum and the other due to an over-pressure at the exit plane caused by the unsteadiness of the jet. The flow immediately downstream of the body in all three modes consists of vortex rings; the differentiating point being the vastly different orientations of the vortex rings. However, since all the bodies are self-propelling, the thrust force must be equal to the drag force (at steady speed), implying no net force on the body, and hence the wake or flow downstream must be momentumless. For such bodies, where there is no net force, it is difficult to directly define a propulsion efficiency, although it is possible to use some other very different measures like “cost of transportation” to broadly judge performance.

Aquatic Ecosystems: Conservation, Restoration and Management

Aquatic Ecosystems perform numerous valuable environmental functions. They recycle nutrients, purify water, recharge ground water, augment and maintain stream flow, and provide habitat for a wide variety of flora and fauna and recreation for people. A rapid population increase accompanied by unplanned developmental works has led to the pollution of surface waters due to residential, agricultural, commercial and industrial wastes/effluents and decline in the number of water bodies. Increased demands for drainage of wetlands have been accommodated by channelisation, resulting in further loss of stream habitat, which has led to aquatic organisms becoming extinct or imperiled in increasing numbers and to the impairment of many beneficial uses of water, including drinking, swimming and fishing. Various anthropogenic activities have altered the physical, chemical and biological processes within aquatic ecosystems. An integrated and accelerated effort toward environmental restoration and preservation is needed to stop further degradation of these fragile ecosystems. Failure to restore these ecosystems will result in sharply increased environmental costs later, in the extinction of species or ecosystem types, and in permanent ecological damage.

The force distribution function of an oscillator model of polymer stretching at constant velocity

Recent simulations of the stretching of tethered biopolymers at a constant speed v (Ponmurugan and Vemparala, 2011 Phys. Rev. E 84 060101(R)) have suggested that for any time t, the distribution of the fluctuating forces f responsible for chain deformation is governed by a relation of the form P(+ f)/ P(- f) = expgamma f], gamma being a coefficient that is solely a function of v and the temperature T. This result, which is reminiscent of the fluctuation theorems applicable to stochastic trajectories involving thermodynamic variables, is derived in this paper from an analytical calculation based on a generalization of Mazonka and Jarzynski's classic model of dragged particle dynamics Mazonka and Jarzynski, 1999 arXiv:cond-\textbackslashmat/9912121v1]. However, the analytical calculations suggest that the result holds only if t >> 1 and the force fluctuations are driven by white rather than colored noise; they further suggest that the coefficient gamma in the purported theorem varies not as v(0.15)T-(0.7), as indicated by the simulations, but as vT(-1).

Computational investigations on covalent dimerization/oligomerization of polyacenes: Is it relevant to soot formation?

We have postulated a novel pathway that could assist in the nucleation of soot particles through covalent dimerization and oligomerizations of a variety of PAHs. DFT calculations were performed with the objective of obtaining the relative thermal stabilities and formation probabilities of oligomeric species that exploit the facile dimerization that is known to occur in linear oligoacenes. We propose that the presence of small stretches of linear oligoacence (tetracene or longer) in extended PAH, either embedded or tethered, would be adequate for enabling the formation of such dimeric and oligomeric adducts; these could then serve as nuclei for the growth of soot particles. Our studies also reveal the importance of p-stacking interactions between extended aromatic frameworks in governing the relative stabilities of the oligomeric species that are formed. (c) 2012 Wiley Periodicals, Inc.

Electromechanical dynamics and optimization of pectoral fin-based ionic polymer-metal composite underwater propulsor

Ionic polymer-metal composites are soft artificial muscle-like bending actuators, which can work efficiently in wet environments such as water. Therefore, there is significant motivation for research on the development and design analysis of ionic polymer-metal composite based biomimetic underwater propulsion systems. Among aquatic animals, fishes are efficient swimmers with advantages such as high maneuverability, high cruising speed, noiseless propulsion, and efficient stabilization. Fish swimming mechanisms provide biomimetic inspiration for underwater propulsor design. Fish locomotion can be broadly classified into body and/or caudal fin propulsion and median and/or paired pectoral fin propulsion. In this article, the paired pectoral fin-based oscillatory propulsion using ionic polymer-metal composite for aquatic propulsor applications is studied. Beam theory and the concept of hydrodynamic function are used to describe the interaction between the beam and water. Furthermore, a quasi-steady blade element model that accounts for unsteady phenomena such as added mass effects, dynamic stall, and the cumulative Wagner effect is used to obtain hydrodynamic performance of the ionic polymer-metal composite propulsor. Dynamic characteristics of ionic polymer-metal composite fin are analyzed using numerical simulations. It is shown that the use of optimization methods can lead to significant improvement in performance of the ionic polymer-metal composite fin.

The Hinge Region of Human Thyroid-Stimulating Hormone (TSH) Receptor Operates as a Tunable Switch between Hormone Binding and Receptor Activation

The mechanism by which the hinge regions of glycoprotein hormone receptors couple hormone binding to activation of downstream effecters is not clearly understood. In the present study, agonistic (311.62) and antagonistic (311.87) monoclonal antibodies (MAbs) directed against the TSH receptor extracellular domain were used to elucidate role of the hinge region in receptor activation. MAb 311.62 which identifies the LRR/Cb-2 junction (aa 265-275), increased the affinity of TSHR for the hormone while concomitantly decreasing its efficacy, whereas MAb 311.87 recognizing LRR 7-9 (aa 201-259) acted as a non-competitive inhibitor of Thyroid stimulating hormone (TSH) binding. Binding of MAbs was sensitive to the conformational changes caused by the activating and inactivating mutations and exhibited differential effects on hormone binding and response of these mutants. By studying the effects of these MAbs on truncation and chimeric mutants of thyroid stimulating hormone receptor (TSHR), this study confirms the tethered inverse agonistic role played by the hinge region and maps the interactions between TSHR hinge region and exoloops responsible for maintenance of the receptor in its basal state. Mechanistic studies on the antibody-receptor interactions suggest that MAb 311.87 is an allosteric insurmountable antagonist and inhibits initiation of the hormone induced conformational changes in the hinge region, whereas MAb 311.62 acts as a partial agonist that recognizes a conformational epitope critical for coupling of hormone binding to receptor activation. The hinge region, probably in close proximity with the alpha-subunit in the hormone-receptor complex, acts as a tunable switch between hormone binding and receptor activation.

Covalently Linked, Water-Dispersible, Cyciodextrin: Reduced-Graphene Oxide Sheets

Reduced-graphene oxide (rGO) sheets have been functionalized by covalently linking beta-cyclodextrin (beta CD) cavities to the sheets via an amide linkage. The functionalized beta-CD:rGO sheets, in contrast to rGO, are dispersible over a wide range of pH values (2-13). Zeta potential measurements indicate that there is more than one factor responsible for the dispersibility. We show here that planar aromatic molecules adsorbed on the rGO sheet as well as nonplanar molecules included in the tethered beta-CD cavities have their fluorescence effectively quenched by the beta-CD:rGO sheets. The beta-CD:rGO sheets combine the hydrophobicity associated with rGO along with the hydrophobicity of the cyclodextrin cavities in a single water-dispersible material.

Fish inspired biomimetic ionic polymer metal composite pectoral fins using labriform propulsion

Ionic polymer metal composites (IPMC) are a new class of smart materials that have attractive characteristics such as muscle like softness, low voltage and power consumption, and good performance in aqueous environments. Thus, IPMC’s provide promising application for biomimetic fish like propulsion systems. In this paper, we design and analyze IPMC underwater propulsor inspired from swimming of Labriform fishes. Different fish species in nature are source of inspiration for different biomimetic flapping IPMC fin design. Here, three fish species with high performance flapping pectoral fin locomotion is chosen and performance analysis of each fin design is done to discover the better configurations for engineering applications. In order to describe the behavior of an active IPMC fin actuator in water, a complex hydrodynamic function is used and structural model of the IPMC fin is obtained by modifying the classical dynamic equation for a slender beam. A quasi-steady blade element model that accounts for unsteady phenomena such as added mass effects, dynamic stall, and the cumulative Wagner effect is used to estimate the hydrodynamic performance of the flapping rectangular shape fin. Dynamic characteristics of IPMC actuated flapping fins having the same size as the actual fins of three different fish species, Gomphosus varius, Scarus frenatus and Sthethojulis trilineata, are analyzed with numerical simulations. Finally, a comparative study is performed to analyze the performance of three different biomimetic IPMC flapping pectoral fins.

Synthesis and characterisation of novel alkoxycyanobiphenyl-substituted rufigallols

Microwave-assisted synthesis of novel alkoxycyanobiphenyl-substituted rufigallols are reported by systematically replacing one, two, four, five or six cyanobiphenyl-tethered alkoxy chains. The synthesis of the target compounds was challenging since classical reactions failed to produce these hybrids. Chemical structures of the hybrids were determined by H-1 nuclear magnetic resonance (NMR), C-13 NMR, infrared, ultraviolet spectroscopy and elemental analysis. The thermotropic liquid crystalline properties of the new compounds were investigated by polarising optical microscopy, differential scanning calorimetry and X-ray diffractometry.