Dynamo onset as a first-order transition: Lessons from a shell model for magnetohydrodynamics

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydro-dynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number Pr-M and the magnetic Reynolds number Re-M. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (Pr-M(-1), Re-M) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

Structure of Ce1-xSnxO2 and its relation to oxygen storage property from first-principles analysis

CeO2-SnO2 solid solution has been reported to possess high oxygen storage/release property which possibly originates from local structural distortion. We have performed first-principles based density functional calculations of Ce1-xSnxO2 structure (x=0, 0.25, 0.5, 1) to understand its structural stability in fluorite in comparison to rutile structure of the other end-member SnO2, and studied the local structural distortion induced by the dopant Sn ion. Analysis of relative energies of fluorite and rutile phases of CeO2, SnO2, and Ce1-xSnxO2 indicates that fluorite structure is the most stable for Ce1-xSnxO2 solid solution. An analysis of local structural distortions reflected in phonon dispersion show that SnO2 in fluorite structure is highly unstable while CeO2 in rutile structure is only weakly unstable. Thus, Sn in Ce1-xSnxO2-fluorite structure is associated with high local structural distortion whereas Ce in Ce1-xSnxO2-rutile structure, if formed, will show only marginal local distortion. Determination of M-O (M=Ce or Sn) bond lengths and analysis of Born effective charges for the optimized structure of Ce1-xSnxO2 show that local coordination of these cations changes from ideal eightfold coordination expected of fluorite lattice to 4+4 coordination, leading to generation of long and short Ce-O and Sn-O bonds in the doped structure. Bond valence analyses for all ions show the presence of oxygen with bond valence similar to 1.84. These weakly bonded oxygen ions are relevant for enhanced oxygen storage/release properties observed in Ce1-xSnxO2 solid solution. (C) 2010 American Institute of Physics.

First passage probability during random vibration

The probability that a random process crosses an arbitrary level for the first time is expressed as a Gram—Charlier series, the leading term of which is the Poisson approximation. The coefficients of this series are related to the moments of the number of level crossings. The results are applicable to both stationary and non-stationary processes. Some numerical results are presented for the response process of a linear single-degree-of-freedom oscillator under Gaussian white noise excitation.

Anisotropy of the Stone-Wales defect and warping of graphene nanoribbons: A first-principles analysis

Stone-Wales (SW) defects, analogous to dislocations in crystals, play an important role in mechanical behavior of sp(2)-bonded carbon based materials. Here, we show using first-principles calculations that a marked anisotropy in the interaction among the SW defects has interesting consequences when such defects are present near the edges of a graphene nanoribbon: depending on their orientation with respect to edge, they result in compressive or tensile stress, and the former is responsible to depression or warping of the graphene nanoribbon. Such warping results in delocalization of electrons in the defect states.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

A fast algorithm for macromolecular packing calculation

An algorithm to improve the computation time of packing calculations for macromolecules is presented. This is achieved by reducing the three-dimensional search to a small set of two-dimensional searches.

Effective treatment of infectious diseases: A nonlinear adaptive control theoretic approach

A nonlinear adaptive system theoretic approach is presented in this paper for effective treatment of infectious diseases that affect various organs of the human body. The generic model used does not represent any specific disease. However, it mimics the generic immunological dynamics of the human body under pathological attack, including the response to external drugs. From a system theoretic point of view, drugs can be interpreted as control inputs. Assuming a set of nominal parameters in the mathematical model, first a nonlinear controller is designed based on the principle of dynamic inversion. This treatment strategy was found to be effective in completely curing "nominal patients". However, in some cases it is ineffective in curing "realistic patients". This leads to serious (sometimes fatal) damage to the affected organ. To make the drug dosage design more effective, a model-following neuro-adaptive control design is carried out using neural networks, which are trained (adapted) online. From simulation studies, this adaptive controller is found to be effective in killing the invading microbes and healing the damaged organ even in the presence of parameter uncertainties and continuing pathogen attack.

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

X-Ray structure of a ternary complex, copper(II)–lnosine 5-monophosphate–benzimidazole. The first example for the absence of direct metal–nucleotide interaction

The unprecedented absence of direct metal–nucleotide interaction has been observed in the X-ray structure of the ternary metal nucleotide system [Cu(bzim)(H2O)5]2+[IMP]2–·3H2O [IMP = inosine 5-monophosphate(2–), bzim = benzimidazole). The complex crystallizes in the space group P21 with a= 7.013(2), b= 13.179(9), c= 14.565(9)Å, = 94.82(4)°, and Z= 2. The structure was solved by the heavy-atom method and refined by full-matrix least squares on the basis of 1 761 observed (I? 3i) reflections to final R and R values of 0.034 and 0.036 respectively. The CuII has a distorted octahedral co-ordination with a nitrogen of the bzim ligand [Cu–N 1.947(5)Å] and three oxygens of water molecules in the basal plane [mean Cu–O 2.017(3)Å] and two more water oxygens at axial positions [Cu–O 2.194(6) and 2.732(5)Å]. The nucleotide base stacks with the bzim ligand at an average distance of 3.5 Å and an angle of 22°. In the lattice, N(7) of the base is linked to a lattice water through a hydrogen bond, while all the phosphate oxygens are involved in hydrogen bonds with co-ordinated as well as lattice water molecules. The co-ordination behaviour of IMP to CuII is compared in structures containing different -aromatic amines in order to assess the influence of the ternary ligand in complex formation. The present results indicate that, apart from the commonly observed phosphate binding, other modes of co-ordination are possible, these being influenced mainly by the -accepting properties of the ternary ligand.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

The first D-pi-A octupolar cryptand molecule to exhibit bulk non-linearity

The cryptand derivative has H-bond mediated trigonal network structure that leads to octupolar bulk nonlinearity.

Calculation of Coulomb interaction strengths for 3d transition metals and actinides

Coulomb interaction strengths (Udd and Uff) have been calculated from Hartree-Fock-Slater atomic calculations for 3d transition and 5f actinide elements, respectively. By decomposing the different contributions to the response (screening) to the 3d charge fluctuation, we show that a substantial reduction in Udd arises due to the relaxation of the 3d charge distribution itself. This, combined with the screening due to the response of the 4s charge density, is shown to provide a very compact screening charge comparable to the metallic case, explaining the success of the atomic calculations for estimating U even in the metals. A pronounced dependence of Udd (or Uff) on the number of electrons nd (nf) or the electronic configuration is also shown here.

The first total synthesis of (+/-)-lagopodin A

The first total synthesis of (±)-lagopodin A and a formal total synthesis of enokipodins A and B is described. The requisite precursors containing two vicinal quaternary carbon atoms were assembled employing Claisen rearrangement and an RCM reaction as key steps starting from 2,5-dimethoxy-4-methylacetophenone.