Fluctuation-dissipation relation for nonlinear Langevin equations

It is shown that the fluctuation-dissipation theorem is satisfied by the solutions of a general set of nonlinear Langevin equations with a quadratic free-energy functional (constant susceptibility) and field-dependent kinetic coefficients, provided the kinetic coefficients satisfy the Onsager reciprocal relations for the irreversible terms and the antisymmetry relations for the reversible terms. The analysis employs a perturbation expansion of the nonlinear terms, and a functional integral calculation of the correlation and response functions, and it is shown that the fluctuation-dissipation relation is satisfied at each order in the expansion.

Highly Efficient and Thermally Stable Second-Order Nonlinear Optical Chromophores and Electrooptic Polymers

Organic polymeric electro-optic (E-O) materials have attracted significant attention because of their potential use as fast and efficient components of integrated photonic devices (1,2). However, the practical application of these materials in optical devices is somewhat limited by the stringent material requirements imposed by the device design, fabrication processes and operating environments. Among the various material requirements, the most notable ones are large electro-optic coefficients (r(33)) and high thermal stability (3). The design of poled polymeric materials with high electro-optic activity (r(33)) involves the optimization of the percent incorporation of efficient (large beta mu) second order nonlinear optical (NLO) chromophores into the polymer matrices and the effective creation of poling-induced non-centrosymmetric structures. The factors that affect the material stability are a) the inherent thermal stability of the NLO chromophores, b) the chemical stability of the NLO chromophores during the polymer processing conditions, and c) the long-term dipolar alignment stability at high temperatures. Although considerable progress has been made in achieving these properties (4), organic polymeric materials suitable for practical E-O device applications are yet to be developed. This chapter highlights some of our approaches in the optimization of molecular and material nonlinear optical and thermal properties.

Hydrogen-Bond-Directed Nonlinear-Optical Organic Materials - Evidence For The Control Of 2nd-Harmonic Generation Activities From The X-Ray Crystal-Structures Of The Complexes Of L-Tartaric Acid With M-Anisidine and P-Toluidine

Several substituted anilines were converted to binary salts with L-tartaric acid. Second harmonic generation (SHG) activities of these salts were determined. The crystal packing in two structures, (i) m-anisidinium-L-tartrate monohydrate (i) and (ii) p-toluidinium-L-tartrate (2), studied using X-ray diffraction demonstrates that extensive hydrogen bonding steers the components into a framework which has a direct bearing on the SHG activity

Methods of nonlinear random vibration analysis

The various techniques available for the analysis of nonlinear systems subjected to random excitations are briefly introduced and an overview of the progress which has been made in this area of research is presented. The discussion is mainly focused on the basis, scope and limitations of the solution techniques and not on specific applications.

Chopped nonlinear magneto-optic rotation: A technique for precision measurements

We have developed a technique for precise measurement of small magnetic fields using nonlinear magneto-optic rotation (NMOR). The technique relies on the resonant laser beam being chopped. During the on time, the atoms are optically pumped into an aligned ground state (Delta m=2 coherence). During the off time, they freely precess around the magnetic field at the Larmor frequency. If the on-off modulation frequency matches (twice) the Larmor precession frequency, the rotation is resonantly enhanced in every cycle, thereby making the process like a repeated Ramsey measurement of the Larmor frequency. We study chopped-NMOR in a paraffin-coated Cs vapor cell. The out-of-phase demodulated rotation shows a Lorentzian peak of linewidth 85 mu G, corresponding to a sensitivity of 0.15nG/root Hz. We discuss the potential of this technique for the measurement of an atomic electric-dipole moment. Copyright (C) EPLA, 2011

Prediction of separation factor in foam separation of proteins

A phenomenological model has been developed for predicting separation factors obtained in concentrating protein solutions using batch-foam columns. The model considers the adsorption of surface active proteins onto the air-water interface of bubbles, and drainage of liquid from the foam, which are the two predominant processes responsible for separation in foam columns. The model has been verified with data collected on casein and bovine serum albumin (BSA) solutions, for which adsorption isotherms are available in the literature. It has been found that an increase in liquid pool height above the gas distributor and the time allowed for drainage result in a better separation. Further, taller foam columns yield poorer separation at constant time of drainage. The model successfully predicts the observed results. (C) 1997 Elsevier Science Ltd.

Prediction of the senses of helical amphiphilic assemblies from effective intermolecular pair potential: Studies on chiral monolayers and bilayers

It is well-known that the senses (or the handedness) of the helical assemblies formed from compressed monolayers and bilayers of chiral amphiphiles are highly specific about the chirality of the monomers concerned. We present here a molecular approach that can successfully predict the senses of such helical morphologies. The present approach is based on a reduced tractable description in terms of an effective pair potential (EPP) which depends on the distance of separation and the relative orientations of the two amphiphiles. This approach explicitly considers the pairwise intermolecular interactions between the groups attached to the chiral centers of the two neighboring amphiphiles. It is found that for a pair of the same kind of enantiomers the minimum energy configuration favors a twist angle between molecules and that this twist from neighbor to neighbor gives rise to the helicity of the aggregate. From the known twist angles at the minimum energy configuration the successive arrangement of an array of molecules can be predicted. Therefore, the sense of the helicity can be predicted from the molecular interactions. The predicted senses of the helical structures are in complete agreement with all known experimental results.

Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called 'symplectic condition' (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

Nonlinear Optical Properties of Stacked Conjugated Systems

We study linear and nonlinear optical properties of two push-pull polyenes stacked in head to head (HtH) and head to tail (HtT) configurations, at different stacking angles within the Pariser-Parr-Pople model using exact diagonalization method. By varying the stacking angle between the polyenes, we find that the optical gap varies marginally, but transition dipoles show large variations. We find that the dominant first-order hyperpolarizability component beta(XXX) for HtH arrangement and beta(YYY) for HtT arrangement strongly depend on the distance of separation between molecules, while the other smaller component beta(XYY) for HtH arrangement and beta(XXY) for HtT arrangement) does not show this variation with distance. We find that the beta(XXX) for HtH configuration shows a maximum at an angle away from 0, in contrast with the oriented gas model. This angle varies with distance between the polyenes, and at large distance it falls to 0. The ratio of all components of beta of a dimer to monomer is less than two for HtH configuration for all angles. But for HtT configurations the ratio of the dominant beta component is greater than two at large angles. Our ZINDO study on two monomers (4-hydroxy-4'-nitroazobenzene) connected in a nonconjugative fashion shows a linear increase in vertical bar(beta) over right arrow (av)vertical bar without much red shift in optical gap. There is a linear increase in vertical bar(beta) over right arrow (av)vertical bar with increase in number of monomers connected nonconjugatively without resulting in a red shift in optical gap.

Nonlinear analysis of adhesively bonded lap joints considering viscoplasticity in adhesives

This paper presents nonlinear finite element analysis of adhesively bonded joints considering the elastoviscoplastic constitutive model of the adhesive material and the finite rotation of the joint. Though the adherends have been assumed to be linearly elastic, the yielding of the adhesive is represented by a pressure sensitive modified von Mises yield function. The stress-strain relation of the adhesive is represented by the Ramberg-Osgood relation. Geometric nonlinearity due to finite rotation in the joint is accounted for using the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor in a total Lagrangian formulation. Critical time steps have been calculated based on the eigenvalues of the transition matrices of the viscoplastic model of the adhesive. Stability of the viscoplastic solution and time dependent behaviour of the joints are examined. A parametric study has been carried out with particular reference to peel and shear stress along the interface. Critical zones for failure of joints have been identified. The study is of significance in the design of lap joints as well as on the characterization of adhesive strength. (C) 1999 Elsevier Science Ltd. All rights reserved.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Nonlinear electrical conduction and broad band noise in the charge-ordered rare earth manganate Nd0.5Ca0.5MnO3

Measurements of the dc transport properties and the low-frequency conductivity noise in films of charge-ordered Nd0.5Ca0.5MnO3 grown on Si substrate reveal the existence of a threshold field in the charge-ordered regime beyond which strong nonlinear conduction sets in along with a large broad band conductivity noise. Threshold-dependent conduction disappears as T --> T-CO, the charge-ordering temperature. This observation suggests that the charge-ordered state gets depinned at the onset of the nonlinear conduction. (C) 1999 American Institute of Physics. [S0003-6951(99)05247-X].

Nonlinear optical activity of anhydrous and hydrated sodium p-nitrophenolate

Differently hydrated sodium p-nitrophenolate (NPNa) crystals were obtained while growing them from different solvents such as methanol and water. Thermal analysis and powder X-ray diffraction studies were carried out on these crystals. Kurtz powder SHG technique was used for qualitative assessment of their nonlinear optical (NLO) activity. From the detailed single-crystal X-ray diffraction studies it is established that NPNa has three different forms, of which only one is found to possess NLO activity. Additionally, a new NLO active crystal was also found to grow from aqueous solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Prediction of reaeration rates in square, stirred tanks

Experiments were conducted on the oxygen transfer coefficient, k(L)a(20), through surface aeration in geometrically similar square tanks, with a rotor of diameter D fitted with six flat blades. An optimal geometric similarity of various linear dimensions, which produced maximum k(L)a(20) for any rotational speed of rotor N by an earlier study, was maintained. A simulation equation uniquely correlating k = k(L)a(20)(nu/g(2))(1/3) (nu and g are kinematic viscosity of water and gravitational constant, respectively), and a parameter governing the theoretical power per unit volume, X = (ND2)-D-3/(g(4/3)nu(1/3)), is developed. Such a simulation equation can be used to predict maximum k for any N in any size of such geometrically similar square tanks. An example illustrating the application of results is presented. Also, it has been established that neither the Reynolds criterion nor the Froude criterion is singularly valid to simulate either k or K = k(L)a(20)/N, simultaneously in all the sizes of tanks, even through they are geometrically similar. Occurrence of "scale effects" due to the Reynolds and the Froude laws of similitude on both k and K are also evaluated.