Phenomenological theory of the kinetics of ultrasonic emulsification

A working model is given for the rate of ultrasonic emulsification, considering the dispersion at the interface (area A) and the coagulations in the volume V of the emulsion. A bimolecular coagulation leads to the equation c=c∞tanh bt;c∞=(Aα/Vβ)1/2;b=(Aαβ/V)1/2 while a monomolecular coagulation gives c=c∞{1-exp (-at)};c∞=Aα/Vβ;a=β. The experiments on the dependence of c∞, a and b upon A and V favour the bimolecular coagulation. The results are satisfactorily explained on general theoretical grounds.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.

Phenomenological aspects of phase fluctuation in high Tc superconductors: Cooper pair droplets

We point out how fluctuation of the phase of the superconducting order parameter can play a key role in our understanding of high Te superconductors. A simple universal criterion is given which illustrates why all oxide superconductors in contrast to classical superconductors ought to behave as a lattice of cooper pairs. T-c is to be thought of as the temperature of phase coherence or the temperature above which the lattice of Cooperpair 'melts' into a phase of Cooper-pair droplets that starts forming at T approximate to T-* . This is the pseudo-gap region. Quantum fluctuation of the phase predicts a superconductor to insulator phase transition for all underdoped materials.

Survey of vector-like fermion extensions of the Standard Model and their phenomenological implications

With the renewed interest in vector-like fermion extensions of the Standard Model, we present here a study of multiple vector-like theories and their phenomenological implications. Our focus is mostly on minimal flavor conserving theories that couple the vector-like fermions to the SM gauge fields and mix only weakly with SM fermions so as to avoid flavor problems. We present calculations for precision electroweak and vector-like state decays, which are needed to investigate compatibility with currently known data. We investigate the impact of vector-like fermions on Higgs boson production and decay, including loop contributions, in a wide variety of vector-like extensions and their parameter spaces.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.

Simple phenomenological determination of contact stiffness and elastic modulus of Ce-based bulk metallic glasses through nanoindentation

The viscoelastic deformation of Ce-based bulk metallic glasses (BMGs) with low glass transition temperature is investigated at room temperature. Contact stiffness and elastic modulus of Ce-based BMGs cannot be derived using the conventional Oliver-Pharr method [W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992)]. The present work shows that the time dependent displacement of unloading segments can be described well by a generalized Kelvin model. Thus, a modified Oliver-Pharr method is proposed to evaluate the contact stiffness and elastic modulus, which does, in fact, reproduce the values obtained via uniaxial compression tests. (c) 2007 American Institute of Physics.

Moderate energy impact analysis combining phenomenological contact law with localised damage and integral equation method

A computational impact analysis methodology has been developed, based on modal analysis and a local contact force-deflection model. The contact law is based on Hertz contact theory while contact stresses are elastic, defines a modified contact theory to take account of local permanent indentation, and considers elastic recovery during unloading. The model was validated experimentally through impact testing of glass-carbon hybrid braided composite panels. Specimens were mounted in a support frame and the contact force was inferred from the deceleration of the impactor, measured by high-speed photography. A Finite Element analysis of the panel and support frame assembly was performed to compute the modal responses. The new contact model performed well in predicting the peak forces and impact durations for moderate energy impacts (15 J), where contact stresses locally exceed the linear elastic limit and damage may be deemed to have occurred. C-scan measurements revealed substantial damage for impact energies in the range of 30-50 J. For this regime the new model predictions might be improved by characterisation of the contact law hysteresis during the unloading phase, and a modification of the elastic vibration response in line with damage levels acquired during the impact. © 2011 Elsevier Ltd. All rights reserved.

Generalized phenomenological model for the viscoelasticity of idealized asphalts

A generalized theory for the viscoelastic behavior of idealized bituminous mixtures (asphalts) is presented. The mathematical model incorporates strain rate and temperature dependency as well as nonmonotonic loading and unloading with shape recovery. The stiffening effect of the aggregate is included. The model is of phenomenological nature. It can be calibrated using a relatively limited set of experimental parameters, obtainable by uniaxial tests. It is shown that the mathematical model can be represented as a special nonlinear form of the Burgers model. This facilitates the derivation of numerical algorithms for solving the constitutive equations. A numerical scheme is implemented in a user material subroutine (UMAT) in the finite-element analysis (FEA) code ABAQUS. Simulation results are compared with uniaxial and indentation tests on an idealized asphalt mix. © 2014 American Society of Civil Engineers.