Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Theory of unitarity bounds and low-energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarily. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K-l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.

A theory on the migration of an extraneous electron across hydrogen bonds in polypeptides

The migrating electrons in biological systems normally are extraneous and taking this into account the electron delocalisation across the hydrogen bonds in proteins is re-examined. It is seen that an extraneous electron can travel rapidly via the low-lying virtual orbitals of the hydrogen-bonded π-electronic structure of peptide units in proteins. The frequency of electron transfer decreases slowly with an increase in the path length. However, the coupling of electron and protonic motions enhances this frequency. Transfer of electrons across the hydrogen bonds in accordance with the double-exchange mechanism does not appear to be possible. This theory offers a possibility for an extraneous electron to transfer within protein structures.

Ultra-fine Grain Materials by Severe Plastic Deformation: Application to Steels

Severe plastic deformation techniques are known to produce grain sizes up to submicron level. This leads to conventional Hall-Petch strengthening of the as-processed materials. In addition, the microstructures of severe plastic deformation processed materials are characterized by relatively lower dislocation density compared to the conventionally processed materials subjected to the same amount of strain. These two aspects taken together lead to many important attributes. Some examples are ultra-high yield and fracture strengths, superplastic formability at lower temperatures and higher strain rates, superior wear resistance, improved high cycle fatigue life. Since these processes are associated with large amount of strain, depending on the strain path, characteristic crystallographic textures develop. In the present paper, a detailed account of underlying mechanisms during SPD has been discussed and processing-microstructure-texture-property relationship has been presented with reference to a few varieties of steels that have been investigated till date.

Effect of Strain Rate on Evolution of the Deformation Microstructure and Texture in Polycrystalline Copper and Nickel

The evolution of crystallographic texture in polycrystalline copper and nickel has been studied. The deformation texture evolution in these two materials over seven orders of magnitude of strain rate from 3 x 10(-4) to similar to 2.0 x 10(+3) s(-1) show little dependence on the stacking fault energy (SFE) and the amount of deformation. Higher strain rate deformation in nickel leads to weakerh < 101 > texture because of extensive microband formation and grain fragmentation. This behavior, in turn, causes less plastic spin and hence retards texture evolution. Copper maintains the stable end < 101 > component over large strain rates (from 3 x 10(-4) to 10(+2) s(-1)) because of its higher strain-hardening rate that resists formation of deformation heterogeneities. At higher strain rates of the order of 2 x 10(+3) s(-1), the adiabatic temperature rise assists in continuous dynamic recrystallization that leads to an increase in the volume fraction of the < 101 > component. Thus, strain-hardening behavior plays a significant role in the texture evolution of face-centered cubic materials. In addition, factors governing the onset of restoration mechanisms like purity and melting point govern texture evolution at high strain rates. SFE may play a secondary role by governing the propensity of cross slip that in turn helps in the activation of restoration processes.

High-Temperature (1023 K to 1273 K 750 degrees C to 1000 degrees C]) Plastic Deformation Behavior of B-Modified Ti-6Al-4V Alloys: Temperature and Strain Rate Effects

A minor addition of B to the Ti-6Al-4V alloy, by similar to 0.1 wt pct, reduces its as-cast prior beta grain size by an order of magnitude, whereas higher B content leads to the presence of in situ formed TiB needles in significant amounts. An experimental investigation into the role played by these microstructural modifications on the high-temperature deformation behavior of Ti-6Al-4V-xB alloys, with x varying between 0 wt pct and 0.55 wt pct, was conducted. Uniaxial compression tests were performed in the temperature range of 1023 K to 1273 K (750 degrees C to 1000 degrees C) and in the strain rate range of 10(-3) to 10(+1) s(-1). True stress-true strain responses of all alloys exhibit flow softening at lower strain rates and oscillations at higher strain rates. The flow softening is aided by the occurrence of dynamic recrystallization through lath globularization in high temperature (1173 K to 1273 K 900 degrees C to 1000 degrees C]) and a lower strain rate (10(-2) to 10(-3) s(-1)) regime. The grain size refinement with the B addition to Ti64, despite being marked, had no significant effect on this. Oscillations in the flow curve at a higher strain rate (10(0) to 10(+1) s(-1)), however, are associated with microstructural instabilities such as bending of laths, breaking of lath boundaries, generation of cavities, and breakage of TiB needles. The presence of TiB needles affected the instability regime. Microstructural evidence suggests that the matrix cavitation is aided by the easy fracture of TiB needles.

Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.

Characterization of hot deformation behavior of brasses using processing maps: Part II. β Brass and α-β brass

The hot deformation behaviors of β brass in the temperature range of 550°C to 800°C and α-β brass in the temperature range of 450°C to 800°C have been characterized in the strain rate range of 0.001 to 100 s−1 using processing maps developed on the basis of the Dynamic Materials Model. The map for β brass revealed a domain of superplasticity in the entire temperature range and at strain rates lower than 1 s−1, with a maximum efficiency of power dissipation of about 68 pct. The temperature variation of the efficiency of power dissipation in the domain is similar to that of the diffusion coefficient for zinc in β brass, confirming that the diffusion-accommodated flow controls the superplasticity. The material undergoes microstructural instability in the form of adiabatic shear bands and strain markings at temperatures lower than 700°C and at strain rates higher than 10 s−1. The map for α-β brass revealed a wide domain for processing in the temperature range of 550°C to 800°C and at strain rates lower than 1 s−1, with a maximum efficiency of 54 pct occurring at about 750°C and 0.001 s−1. In the domain, the α phase undergoes dynamic recrystallization and controls the hot deformation of the alloy, while the β phase deforms superplastically. At strain rates greater than 1 s−1, α-β brass exhibits microstructural instabilities manifested as flow rotations at lower temperatures and localized shear bands at higher temperatures.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. I. Theory

Based on a method proposed by Reddy and Daum, the equations governing the steady inviscid nonreacting gasdynamic laser (GDL) flow in a supersonic nozzle are reduced to a universal form so that the solutions depend on a single parameter which combines all the other parameters of the problem. Solutions are obtained for a sample case of available data and compared with existing results to validate the present approach. Also, similar solutions for a sample case are presented.

Molecular hydrodynamic theory of non‐Markovian collective orientational relaxation in dense dipolar liquids

A microscopic study of the non‐Markovian (or memory) effects on the collective orientational relaxation in a dense dipolar liquid is carried out by using an extended hydrodynamic approach which provides a reliable description of the dynamical processes occuring at the molecular length scales. Detailed calculations of the wave‐vector dependent orientational correlation functions are presented. The memory effects are found to play an important role; the non‐Markovian results differ considerably from that of the Markovian theory. In particular, a slow long‐time decay of the longitudinal orientational correlation function is observed for dense liquids which becomes weaker in the presence of a sizeable translational contribution to the collective orientational relaxation. This slow decay can be attributed to the intermolecular correlations at the molecular length scales. The longitudinal component of the orientational correlation function becomes oscillatory in the underdamped limit of momenta relaxations and the frequency dependence of the friction reduce the frictional resistance on the collective excitations (commonly known as dipolarons) to make them long lived. The theory predicts that these dipolarons can, therefore, be important in chemical relaxation processes, in contradiction to the claims of some earlier theoretical studies.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.