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## Full-Text Articles in Physics

Nonlinear Ordinary Differential Equations In Fluid Dynamics, John D. Ramshaw

#### Nonlinear Ordinary Differential Equations In Fluid Dynamics, John D. Ramshaw

*Physics Faculty Publications and Presentations*

The equivalence between nonlinear ordinary differential equations (ODEs) and linear partial differential equations (PDEs) was recently revisited by Smith, who used the equivalence to transform the ODEs of Newtonian dynamics into equivalent PDEs, from which analytical solutions to several simple dynamical problems were derived. We show how this equivalence can be used to derive a variety of exact solutions to the PDEs describing advection in fluid dynamics in terms of solutions to the equivalent ODEs for the trajectories of Lagrangian fluid particles. The PDEs that we consider describe the time evolution of non-diffusive scalars, conserved densities, and Lagrangian surfaces advected ...

Whispering-Gallery Acoustic Sensing: Characterization Of Mesoscopic Films And Scanning Probe Microscopy Applications, Andres H. La Rosa, Nan Li, Rodolfo Fernandez, Xiaohua Wang, Richard Nordstrom, S. K. Padigi

#### Whispering-Gallery Acoustic Sensing: Characterization Of Mesoscopic Films And Scanning Probe Microscopy Applications, Andres H. La Rosa, Nan Li, Rodolfo Fernandez, Xiaohua Wang, Richard Nordstrom, S. K. Padigi

*Physics Faculty Publications and Presentations*

Full understanding of the physics underlying the striking changes in viscoelasticity, relaxation time, and phase transitions that mesoscopic fluid-like films undergo at solid-liquid interfaces, or under confinement between two sliding solid boundaries, constitutes one of the major challenges in condensed matter physics. Their role in the imaging process of solid substrates by scanning probe microscopy (SPM) is also currently controversial. Aiming at improving the reliability and versatility of instrumentation dedicated to characterize mesoscopic films, a noninvasive whispering-gallery acoustic sensing (WGAS) technique is introduced; its application as feedback control in SPM is also demonstrated. To illustrate its working principle and potential ...

Dynamical Evolution Of Volume Fractions In Multipressure Multiphase Flow Models, C. H. Chang, John D. Ramshaw

#### Dynamical Evolution Of Volume Fractions In Multipressure Multiphase Flow Models, C. H. Chang, John D. Ramshaw

*Physics Faculty Publications and Presentations*

Compared to single-pressure models, multipressure multiphase flow models require additional closure relations to determine the individual pressures of the different phases. These relations are often taken to be evolution equations for the volume fractions. We present a rigorous theoretical framework for constructing such equations for compressible multiphase mixtures in terms of submodels for the relative volumetric expansion rates ∆Ei of the phases. These quantities are essentially the rates at which the phases dynamically expand or contract in response to pressure differences, and represent the general tendency of the volume fractions to relax toward values that produce local pressure equilibrium. We ...

Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces In Spherical Geometry, John D. Ramshaw

#### Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces In Spherical Geometry, John D. Ramshaw

*Physics Faculty Publications and Presentations*

A simple model was recently described for predicting linear and nonlinear mixing at an unstable planar fluid interface subjected to an arbitrary time-dependent variable acceleration history [J. D. Ramshaw, Phys. Rev. E 58, 5834 (1998)]. Here we present an analogous model for describing the mixing of two adjacent spherical fluid shells of different density resulting from an arbitrary time-dependent mean interface radius R(t). As in the planar case, the model is based on a heuristic expression for the kinetic energy of the system. This expression is based on that for the kinetic energy of a linearly perturbed interface, but ...

Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces With Variable Acceleration, John D. Ramshaw

#### Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces With Variable Acceleration, John D. Ramshaw

*Physics Faculty Publications and Presentations*

A simple model is described for predicting the time evolution of the half-width h of a mixing layer between two initially separated immiscible fluids of different density subjected to an arbitrary time-dependent variable acceleration history a(t). The model is based on a heuristic expression for the kinetic energy per unit area of the mixing layer. This expression is based on that for the kinetic energy of a linearly perturbed interface, but with a dynamically renormalized wavelength which becomes proportional to h in the nonlinear regime. An equation of motion for h is then derived from Lagrange's equations. This ...

Self-Consistent Effective Binary Interaction Approximation For Strongly Coupled Multifluid Dynamics, John D. Ramshaw

#### Self-Consistent Effective Binary Interaction Approximation For Strongly Coupled Multifluid Dynamics, John D. Ramshaw

*Physics Faculty Publications and Presentations*

An improved self-consistent effective binary diffusion approximation for multicomponent diffusion was recently described [1]. Here we develop an analogous self-consistent effective binary interaction (SCEBI) approximation for simplifying multifluid dynamical descriptions in which each fluid is strongly coupled to the other fluids by pairwise frictional forces. The net drag force on each fluid is the summation of the drag forces due to each of the other fluids. This summation is approximated by a single term proportional to the velocity of the fluid in question relative to an appropriately weighted average velocity. This approximation permits an explicit numerical solution for the fluid ...

Existence Of The Dielectric Constant In Dipolar Fluid Mixtures, John D. Ramshaw, Norman D. Hamer

#### Existence Of The Dielectric Constant In Dipolar Fluid Mixtures, John D. Ramshaw, Norman D. Hamer

*Physics Faculty Publications and Presentations*

The existence of the dielectric constant epsilon is investigated for fluid mixtures of rigid polar molecules. The investigation is performed using the functional-derivative formalism for mixtures, and is closely analogous to that previously carried out for pure dipolar fluids (J. Chem. Phys. 68, 5199 (1978)). Sufficient conditions for the existence of epsilon are obtained in terms of the direct correlation function matrix c/sub alphabeta/(12). It is found that epsilon exists if c/sub alphabeta/(12) depends only on relative positions and orientations, and becomes asymptotic to -theta/sub alphabeta/(12)/kT at long range, where theta/sub alphabeta ...

Brownian Motion In A Flowing Fluid Revisited, John D. Ramshaw

#### Brownian Motion In A Flowing Fluid Revisited, John D. Ramshaw

*Physics Faculty Publications and Presentations*

It is shown how the phenomenon of osmosis may be treated using the phenomenological theory of Brownian motion in a flowing fluid. The theory is also generalized to include viscous stresses in the particle and mixture momentum equations.

Partial Chemical Equilibrium In Fluid Dynamics, John D. Ramshaw

#### Partial Chemical Equilibrium In Fluid Dynamics, John D. Ramshaw

*Physics Faculty Publications and Presentations*

An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates ω [subscript s] for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the ω [subscript s] are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions ...

Existence Of The Dielectric Constant In Rigid-Dipole Fluids: The Functional-Derivative Approach, John D. Ramshaw

#### Existence Of The Dielectric Constant In Rigid-Dipole Fluids: The Functional-Derivative Approach, John D. Ramshaw

*Physics Faculty Publications and Presentations*

In a previous article [J. Chem. Phys. 57, 2684 (1972)] sufficient conditions were established for the existence of the dielectric constant ɛ in rigid-dipole fluids. One of these conditions was an unrealistic restriction on the angular dependence of the direct correlation function c (12) at short range. Here it is shown that this restriction can be removed without altering the previous conclusions. Consequently, ɛ rigorously exists if c (12) depends only upon relative positions and orientations of molecules 1 and 2, and becomes asymptotic to -φd(12)/kT at long range, where φd(12) is the dipole-dipole potential. The development ...

Existence Of The Dielectric Constant In Rigid-Dipole Fluids: The Direct Correlation Function, John D. Ramshaw

#### Existence Of The Dielectric Constant In Rigid-Dipole Fluids: The Direct Correlation Function, John D. Ramshaw

*Physics Faculty Publications and Presentations*

The question of whether the dielectric constant ε exists (is well defined) for a finite fluid system of rigid dipolar molecules is reconsidered and reformulated. It is found that this question can most simply be expressed in terms of the behavior of the position‐ and orientation‐dependent *direct *correlation function c(r_{1},ω_{1}; r_{2}, ω_{2}). It is shown that ε exists if *c* satisfies the following two conditions: (a) c~–φ/kT for |r_{1}–r_{2}|>σ, where φ is the dipole‐dipole potential and σ is a length which is large microscopically but small ...